Density of Probability of an Electron near the Nucleus Daniel Hercules @ 2010 July 20th
<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>In many situations is necesary to calculate the density of probability to find an electron near the nucleus. In this short article we calculate such probabilities in order to avoid the calculations and simplifications behind the problem. Due to the purpose of this article I will only expose the method to get the result for the s orbitals. The calculations can be easily arranged to produce the same results for other types of orbitals such as the p or d orbitals.JSFH
<Text-field style="Heading 1" layout="Heading 1">Analysis</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGPC8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZTRjpGPQ==Definition of the Radial Wave Function R[n,l]. The first step is to define the parameters that are the ones that tell us which Radial Wave Function (RWF) we need to use in the calculation. In this case we don't need to place much attention to define the variables due to the fact that we are declaring the identity of the RWF. For the effects of this application and to simplify the calculations and open the door for this document to experience some modifications by the user (leading to a better user experience) I am going to include the wave functions from 1s to 3d, 3 being the greatest value that n can take and 2 the greatest value that l can take. In this case, the notation R[n,l] is going to change to R[#,#] with the first digit the n number and the second one the l number that we choose for the calculation.
<Text-field style="Heading 1" layout="Heading 1">Collection of the Radial Wave Functions (RWF)</Text-field>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 of P (dimension less parameter): This is defined as the following identity. As explained before, A is the Bohr Radius while R is the radius that we want to consider in our calculations. In this case, just to show the application of this maple simulation, we are going to choose R as zero just because the purpose of our calculations are defined as "to obtain the probability density at the nucleus for an electron" that has some parameters such as n, l and m. 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
<Text-field style="Heading 1" layout="Heading 1">Collection of the Spherical Harmonic Functions (SHF)</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMEYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRkEvJStleGVjdXRhYmxlR0ZNRkUvJS9zdWJzY3JpcHRzaGlmdEdGRC1GSDYtUSM6PUYnRkVGSy9GT0ZNRlBGUkZURlZGWC9GZW5RLDAuMjc3Nzc3OGVtRicvRmhuRmNvLUYjNictRiw2JVEpc2ltcGxpZnlGJ0Y5RjwtRkg2LVEwJkFwcGx5RnVuY3Rpb247RidGRUZLRmFvRlBGUkZURlZGWEZaL0ZobkZmbi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUklbXN1cEdGJDYlLUZfcDYkLUkmbWZyYWNHRiQ2KC1GIzYlLUZCNiRRIjFGJ0ZFRmpuRkUtRiM2J0YrLUYjNiYtRkI2JFEiNEYnRkUtRkg2LVExJkludmlzaWJsZVRpbWVzO0YnRkVGS0Zhb0ZQRlJGVEZWRlhGWkZdcC1GLDYlUScmIzk2MDtGJy9GOkZNRkVGRUYrRmpuRkUvJS5saW5ldGhpY2tuZXNzR0ZfcS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zici8lKWJldmVsbGVkR0ZNRkUtRmlwNihGW3EtRiM2JS1GQjYkUSIyRidGRUZqbkZFRl5yRmByRmNyRmVyLyUxc3VwZXJzY3JpcHRzaGlmdEdGREZqbkZFRkVGam5GRUYrRmpuRkVGK0ZqbkZFRitGam5GRQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMUYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZCNiRRIjBGJ0ZFLyUrZXhlY3V0YWJsZUdGTUZFLyUvc3Vic2NyaXB0c2hpZnRHRlxvLUZINi1RIzo9RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GZm8tRiM2Jy1GLDYlUSlzaW1wbGlmeUYnRjlGPC1GSDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZFRktGZG9GUEZSRlRGVkZYRlovRmhuRmZuLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GIzYnLUklbXN1cEdGJDYlLUZicDYkLUkmbWZyYWNHRiQ2KC1GIzYlLUZCNiRRIjNGJ0ZFRl1vRkUtRiM2J0YrLUYjNiYtRkI2JFEiNEYnRkUtRkg2LVExJkludmlzaWJsZVRpbWVzO0YnRkVGS0Zkb0ZQRlJGVEZWRlhGWkZgcC1GLDYlUScmIzk2MDtGJy9GOkZNRkVGRUYrRl1vRkUvJS5saW5ldGhpY2tuZXNzR0ZELyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmdyLyUpYmV2ZWxsZWRHRk1GRS1GXnE2KC1GIzYlRkFGXW9GRS1GIzYlLUZCNiRRIjJGJ0ZFRl1vRkVGY3JGZXJGaHJGanIvJTFzdXBlcnNjcmlwdHNoaWZ0R0Zcb0Zcci1GIzYnLUYsNiVRJGNvc0YnRmJyRkVGXXAtRmJwNiQtRiM2JS1GLDYlUScmIzk1MjtGJ0ZickZFRl1vRkVGRUZdb0ZFRitGRUYrRl1vRkVGRUZdb0ZFRitGXW9GRUYrRl1vRkVGK0Zdb0ZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMUYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRkEvJStleGVjdXRhYmxlR0ZNRkUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GSDYtUSM6PUYnRkVGSy9GT0ZNRlBGUkZURlZGWC9GZW5RLDAuMjc3Nzc3OGVtRicvRmhuRmRvLUYjNictRiw2JVEpc2ltcGxpZnlGJ0Y5RjwtRkg2LVEwJkFwcGx5RnVuY3Rpb247RidGRUZLRmJvRlBGUkZURlZGWEZaL0ZobkZmbi1JKG1mZW5jZWRHRiQ2JC1GIzYnRistRiM2Jy1GSDYtUSomdW1pbnVzMDtGJ0ZFRktGYm9GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GanAtRiM2KC1JJW1zdXBHRiQ2JS1GYHA2JC1JJm1mcmFjR0YkNigtRiM2JS1GQjYkUSIzRidGRUZqbkZFLUYjNidGKy1GIzYmLUZCNiRRIjhGJ0ZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGYm9GUEZSRlRGVkZYRlpGXnAtRiw2JVEnJiM5NjA7RicvRjpGTUZFRkVGK0ZqbkZFLyUubGluZXRoaWNrbmVzc0dGRC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zdcy8lKWJldmVsbGVkR0ZNRkUtRmRxNigtRiM2JUZBRmpuRkUtRiM2JS1GQjYkUSIyRidGRUZqbkZFRmlyRltzRl5zRmBzLyUxc3VwZXJzY3JpcHRzaGlmdEdGXm9GYnItRiM2Jy1GLDYlUSRzaW5GJ0ZockZFRltwLUZgcDYkLUYjNiUtRiw2JVEnJiM5NTI7RidGaHJGRUZqbkZFRkVGam5GRUZici1GX3E2JS1GSDYtUS8mRXhwb25lbnRpYWxFO0YnRkVGS0Zib0ZQRlJGVEZWRlhGWi9GaG5RLDAuMTExMTExMWVtRictRiM2Ji1GLDYlUSJpRidGOUY8RmJyLUYsNiVRJyYjOTY2O0YnRmhyRkVGRUZbdEZFRitGam5GRUYrRmpuRkVGRUZqbkZFRitGam5GRUYrRmpuRkVGK0ZqbkZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUkjbW5HRiQ2JFEiMUYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiYtRkg2LVEqJnVtaW51czA7RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GYW9GQS8lK2V4ZWN1dGFibGVHRk1GRUYrRmNvRkUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GSDYtUSM6PUYnRkVGS0Zfb0ZQRlJGVEZWRlgvRmVuUSwwLjI3Nzc3NzhlbUYnL0ZobkZccC1GIzYnLUYsNiVRKXNpbXBsaWZ5RidGOUY8LUZINi1RMCZBcHBseUZ1bmN0aW9uO0YnRkVGS0Zfb0ZQRlJGVEZWRlhGWi9GaG5GZm4tSShtZmVuY2VkR0YkNiQtRiM2J0YrLUYjNigtSSVtc3VwR0YkNiUtRmhwNiQtSSZtZnJhY0dGJDYoLUYjNiUtRkI2JFEiM0YnRkVGY29GRS1GIzYnRistRiM2Ji1GQjYkUSI4RidGRS1GSDYtUTEmSW52aXNpYmxlVGltZXM7RidGRUZLRl9vRlBGUkZURlZGWEZaRmZwLUYsNiVRJyYjOTYwO0YnL0Y6Rk1GRUZFRitGY29GRS8lLmxpbmV0aGlja25lc3NHRkQvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXXMvJSliZXZlbGxlZEdGTUZFLUZkcTYoLUYjNiVGQUZjb0ZFLUYjNiUtRkI2JFEiMkYnRkVGY29GRUZpckZbc0Zec0Zgcy8lMXN1cGVyc2NyaXB0c2hpZnRHRmdvRmJyLUYjNictRiw2JVEkc2luRidGaHJGRUZjcC1GaHA2JC1GIzYlLUYsNiVRJyYjOTUyO0YnRmhyRkVGY29GRUZFRmNvRkVGYnItRl9xNiUtRkg2LVEvJkV4cG9uZW50aWFsRTtGJ0ZFRktGX29GUEZSRlRGVkZYRlovRmhuUSwwLjExMTExMTFlbUYnLUYjNidGXG8tRiM2Ji1GLDYlUSJpRidGOUY8RmJyLUYsNiVRJyYjOTY2O0YnRmhyRkVGRUYrRmNvRkVGW3RGRUYrRmNvRkVGRUZjb0ZFRitGY29GRUYrRmNvRkVGK0Zjb0ZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMkYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZCNiRRIjBGJ0ZFLyUrZXhlY3V0YWJsZUdGTUZFLyUvc3Vic2NyaXB0c2hpZnRHRlxvLUZINi1RIzo9RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GZm8tRiM2Jy1GLDYlUSlzaW1wbGlmeUYnRjlGPC1GSDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZFRktGZG9GUEZSRlRGVkZYRlovRmhuRmZuLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GIzYmLUklbXN1cEdGJDYlLUZicDYkLUkmbWZyYWNHRiQ2KC1GIzYlLUZCNiRRIjVGJ0ZFRl1vRkUtRiM2J0YrLUYjNiYtRkI2JFEjMTZGJ0ZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGZG9GUEZSRlRGVkZYRlpGYHAtRiw2JVEnJiM5NjA7RicvRjpGTUZFRkVGK0Zdb0ZFLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zoci8lKWJldmVsbGVkR0ZNRkUtRl5xNigtRiM2JS1GQjYkRmVyRkVGXW9GRS1GIzYlRkFGXW9GRUZjckZmckZpckZbcy8lMXN1cGVyc2NyaXB0c2hpZnRHRlxvRlxyLUZicDYkLUYjNidGKy1GIzYnLUZCNiRRIjNGJ0ZFRlxyLUYjNiQtRmlwNiUtRiM2Jy1GLDYlUSRjb3NGJ0ZickZFRl1wLUZicDYkLUYjNiUtRiw2JVEnJiM5NTI7RidGYnJGRUZdb0ZFRkVGXW9GRUZBRmVzRkVGK0ZFLUZINi1RKCZtaW51cztGJ0ZFRktGZG9GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GZHVGYXNGRUZFRkVGK0Zdb0ZFRkVGXW9GRUYrRl1vRkVGK0Zdb0ZFRitGXW9GRQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUkjbW5HRiQ2JFEiMkYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiYtRkg2LVEqJnVtaW51czA7RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GYW8tRkI2JFEiMUYnRkUvJStleGVjdXRhYmxlR0ZNRkVGK0Zmb0ZFLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkg2LVEjOj1GJ0ZFRktGX29GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GX3AtRiM2Jy1GLDYlUSlzaW1wbGlmeUYnRjlGPC1GSDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZFRktGX29GUEZSRlRGVkZYRlovRmhuRmZuLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GIzYqLUklbXN1cEdGJDYlLUZbcTYkLUkmbWZyYWNHRiQ2KC1GIzYlLUZCNiRRIzE1RidGRUZmb0ZFLUYjNidGKy1GIzYmLUZCNiRRIjhGJ0ZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGX29GUEZSRlRGVkZYRlpGaXAtRiw2JVEnJiM5NjA7RicvRjpGTUZFRkVGK0Zmb0ZFLyUubGluZXRoaWNrbmVzc0dGZW8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYHMvJSliZXZlbGxlZEdGTUZFLUZncTYoLUYjNiVGY29GZm9GRS1GIzYlRkFGZm9GRUZcc0Zec0Zhc0Zjcy8lMXN1cGVyc2NyaXB0c2hpZnRHRmpvRmVyLUYjNictRiw2JVEkY29zRidGW3NGRUZmcC1GW3E2JC1GIzYlLUYsNiVRJyYjOTUyO0YnRltzRkVGZm9GRUZFRmZvRkVGZXItRiM2Jy1GLDYlUSRzaW5GJ0Zbc0ZFRmZwRmJ0RmZvRkVGZXItRmJxNiUtRkg2LVEvJkV4cG9uZW50aWFsRTtGJ0ZFRktGX29GUEZSRlRGVkZYRlovRmhuUSwwLjExMTExMTFlbUYnLUYjNiYtRiw2JVEiaUYnRjlGPEZlci1GLDYlUScmIzk2NjtGJ0Zbc0ZFRkVGW3RGRUYrRmZvRkVGRUZmb0ZFRitGZm9GRUYrRmZvRkVGK0Zmb0ZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMkYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZCNiRRIjFGJ0ZFLyUrZXhlY3V0YWJsZUdGTUZFLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkg2LVEjOj1GJ0ZFRksvRk9GTUZQRlJGVEZWRlgvRmVuUSwwLjI3Nzc3NzhlbUYnL0ZobkZnby1GIzYnLUYsNiVRKXNpbXBsaWZ5RidGOUY8LUZINi1RMCZBcHBseUZ1bmN0aW9uO0YnRkVGS0Zlb0ZQRlJGVEZWRlhGWi9GaG5GZm4tSShtZmVuY2VkR0YkNiQtRiM2J0YrLUYjNictRkg2LVEqJnVtaW51czA7RidGRUZLRmVvRlBGUkZURlZGWC9GZW5RLDAuMjIyMjIyMmVtRicvRmhuRl1xLUYjNiotSSVtc3VwR0YkNiUtRmNwNiQtSSZtZnJhY0dGJDYoLUYjNiUtRkI2JFEjMTVGJ0ZFRl1vRkUtRiM2J0YrLUYjNiYtRkI2JFEiOEYnRkUtRkg2LVExJkludmlzaWJsZVRpbWVzO0YnRkVGS0Zlb0ZQRlJGVEZWRlhGWkZhcC1GLDYlUScmIzk2MDtGJy9GOkZNRkVGRUYrRl1vRkUvJS5saW5ldGhpY2tuZXNzR0Zcby8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zgcy8lKWJldmVsbGVkR0ZNRkUtRmdxNigtRiM2JUZqbkZdb0ZFLUYjNiVGQUZdb0ZFRlxzRl5zRmFzRmNzLyUxc3VwZXJzY3JpcHRzaGlmdEdGYW9GZXItRiM2Jy1GLDYlUSRjb3NGJ0Zbc0ZFRl5wLUZjcDYkLUYjNiUtRiw2JVEnJiM5NTI7RidGW3NGRUZdb0ZFRkVGXW9GRUZlci1GIzYnLUYsNiVRJHNpbkYnRltzRkVGXnBGYnRGXW9GRUZlci1GYnE2JS1GSDYtUS8mRXhwb25lbnRpYWxFO0YnRkVGS0Zlb0ZQRlJGVEZWRlhGWi9GaG5RLDAuMTExMTExMWVtRictRiM2J0ZpcC1GIzYmLUYsNiVRImlGJ0Y5RjxGZXItRiw2JVEnJiM5NjY7RidGW3NGRUZFRitGXW9GRUZbdEZFRitGXW9GRUYrRl1vRkVGRUZdb0ZFRitGXW9GRUYrRl1vRkVGK0Zdb0ZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMkYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRkEvJStleGVjdXRhYmxlR0ZNRkUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GSDYtUSM6PUYnRkVGSy9GT0ZNRlBGUkZURlZGWC9GZW5RLDAuMjc3Nzc3OGVtRicvRmhuRmRvLUYjNictRiw2JVEpc2ltcGxpZnlGJ0Y5RjwtRkg2LVEwJkFwcGx5RnVuY3Rpb247RidGRUZLRmJvRlBGUkZURlZGWEZaL0ZobkZmbi1JKG1mZW5jZWRHRiQ2JC1GIzYnRistRiM2KC1JJW1zdXBHRiQ2JS1GYHA2JC1JJm1mcmFjR0YkNigtRiM2JS1GQjYkUSMxNUYnRkVGam5GRS1GIzYnRistRiM2Ji1GQjYkUSMzMkYnRkUtRkg2LVExJkludmlzaWJsZVRpbWVzO0YnRkVGS0Zib0ZQRlJGVEZWRlhGWkZecC1GLDYlUScmIzk2MDtGJy9GOkZNRkVGRUYrRmpuRkUvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmZyLyUpYmV2ZWxsZWRHRk1GRS1GXHE2KC1GIzYlLUZCNiRGY3JGRUZqbkZFLUYjNiVGQUZqbkZFRmFyRmRyRmdyRmlyLyUxc3VwZXJzY3JpcHRzaGlmdEdGXm9GanEtRiM2JC1GZ3A2JS1GIzYnLUYsNiVRJHNpbkYnRmByRkVGW3AtRmBwNiQtRiM2JS1GLDYlUScmIzk1MjtGJ0ZgckZFRmpuRkVGRUZqbkZFRkFGY3NGRUZqcS1GZ3A2JS1GSDYtUS8mRXhwb25lbnRpYWxFO0YnRkVGS0Zib0ZQRlJGVEZWRlhGWi9GaG5RLDAuMTExMTExMWVtRictRiM2KEZBRmpxLUYsNiVRImlGJ0Y5RjxGanEtRiw2JVEnJiM5NjY7RidGYHJGRUZFRmNzRkVGK0ZqbkZFRkVGam5GRUYrRmpuRkVGK0ZqbkZFRitGam5GRQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUkjbW5HRiQ2JFEiMkYnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiYtRkg2LVEqJnVtaW51czA7RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GYW9GQS8lK2V4ZWN1dGFibGVHRk1GRUYrRmNvRkUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GSDYtUSM6PUYnRkVGS0Zfb0ZQRlJGVEZWRlgvRmVuUSwwLjI3Nzc3NzhlbUYnL0ZobkZccC1GIzYnLUYsNiVRKXNpbXBsaWZ5RidGOUY8LUZINi1RMCZBcHBseUZ1bmN0aW9uO0YnRkVGS0Zfb0ZQRlJGVEZWRlhGWi9GaG5GZm4tSShtZmVuY2VkR0YkNiQtRiM2J0YrLUYjNigtSSVtc3VwR0YkNiUtRmhwNiQtSSZtZnJhY0dGJDYoLUYjNiUtRkI2JFEjMTVGJ0ZFRmNvRkUtRiM2J0YrLUYjNiYtRkI2JFEjMzJGJ0ZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGX29GUEZSRlRGVkZYRlpGZnAtRiw2JVEnJiM5NjA7RicvRjpGTUZFRkVGK0Zjb0ZFLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zecy8lKWJldmVsbGVkR0ZNRkUtRmRxNigtRiM2JS1GQjYkRltzRkVGY29GRS1GIzYlRkFGY29GRUZpckZcc0Zfc0Zhcy8lMXN1cGVyc2NyaXB0c2hpZnRHRmdvRmJyLUYjNiQtRl9xNiUtRiM2Jy1GLDYlUSRzaW5GJ0ZockZFRmNwLUZocDYkLUYjNiUtRiw2JVEnJiM5NTI7RidGaHJGRUZjb0ZFRkVGY29GRUZBRlt0RkVGYnItRl9xNiUtRkg2LVEvJkV4cG9uZW50aWFsRTtGJ0ZFRktGX29GUEZSRlRGVkZYRlovRmhuUSwwLjExMTExMTFlbUYnLUYjNidGXG8tRiM2KEZBRmJyLUYsNiVRImlGJ0Y5RjxGYnItRiw2JVEnJiM5NjY7RidGaHJGRUZFRitGY29GRUZbdEZFRitGY29GRUZFRmNvRkVGK0Zjb0ZFRitGY29GRUYrRmNvRkU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiM0YnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZCNiRRIjBGJ0ZFLyUrZXhlY3V0YWJsZUdGTUZFLyUvc3Vic2NyaXB0c2hpZnRHRlxvLUZINi1RIzo9RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GZm8tRiM2Jy1GLDYlUSlzaW1wbGlmeUYnRjlGPC1GSDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZFRktGZG9GUEZSRlRGVkZYRlovRmhuRmZuLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GIzYmLUklbXN1cEdGJDYlLUZicDYkLUkmbWZyYWNHRiQ2KC1GIzYlLUZCNiRRIjdGJ0ZFRl1vRkUtRiM2J0YrLUYjNiYtRkI2JFEjMTZGJ0ZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGZG9GUEZSRlRGVkZYRlpGYHAtRiw2JVEnJiM5NjA7RicvRjpGTUZFRkVGK0Zdb0ZFLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zoci8lKWJldmVsbGVkR0ZNRkUtRl5xNigtRiM2JS1GQjYkRmVyRkVGXW9GRS1GIzYlLUZCNiRRIjJGJ0ZFRl1vRkVGY3JGZnJGaXJGW3MvJTFzdXBlcnNjcmlwdHNoaWZ0R0Zcb0Zcci1GYnA2JC1GIzYoRistRiM2Jy1GQjYkUSI1RidGRUZcci1GIzYkLUZpcDYlLUYjNictRiw2JVEkY29zRidGYnJGRUZdcC1GYnA2JC1GIzYlLUYsNiVRJyYjOTUyO0YnRmJyRkVGXW9GRUZFRl1vRkVGQUZoc0ZFRitGRS1GSDYtUSgmbWludXM7RidGRUZLRmRvRlBGUkZURlZGWC9GZW5RLDAuMjIyMjIyMmVtRicvRmhuRmd1LUYjNidGQUZcckZndEYrRkVGK0ZFRkVGRUYrRl1vRkVGRUZdb0ZFRitGXW9GRUYrRl1vRkVGK0Zdb0ZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiM0YnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZCNiRRIjFGJ0ZFLyUrZXhlY3V0YWJsZUdGTUZFLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkg2LVEjOj1GJ0ZFRksvRk9GTUZQRlJGVEZWRlgvRmVuUSwwLjI3Nzc3NzhlbUYnL0ZobkZnby1GIzYnLUYsNiVRKXNpbXBsaWZ5RidGOUY8LUZINi1RMCZBcHBseUZ1bmN0aW9uO0YnRkVGS0Zlb0ZQRlJGVEZWRlhGWi9GaG5GZm4tSShtZmVuY2VkR0YkNiQtRiM2J0YrLUYjNictRkg2LVEqJnVtaW51czA7RidGRUZLRmVvRlBGUkZURlZGWC9GZW5RLDAuMjIyMjIyMmVtRicvRmhuRl1xLUYjNiotSSVtc3VwR0YkNiUtRmNwNiQtSSZtZnJhY0dGJDYoLUYjNiUtRkI2JFEjMjFGJ0ZFRl1vRkUtRiM2J0YrLUYjNiYtRkI2JFEjNjRGJ0ZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGZW9GUEZSRlRGVkZYRlpGYXAtRiw2JVEnJiM5NjA7RicvRjpGTUZFRkVGK0Zdb0ZFLyUubGluZXRoaWNrbmVzc0dGXG8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYHMvJSliZXZlbGxlZEdGTUZFLUZncTYoLUYjNiVGam5GXW9GRS1GIzYlLUZCNiRRIjJGJ0ZFRl1vRkVGXHNGXnNGYXNGY3MvJTFzdXBlcnNjcmlwdHNoaWZ0R0Zhb0Zlci1GY3A2JC1GIzYnRistRiM2Jy1GQjYkUSI1RidGRUZlci1GIzYnLUYsNiVRJGNvc0YnRltzRkVGXnAtRmNwNiQtRiM2JS1GLDYlUScmIzk1MjtGJ0Zbc0ZFRl1vRkVGRUZdb0ZFRitGRS1GSDYtUSgmbWludXM7RidGRUZLRmVvRlBGUkZURlZGWEZccUZecUZqbkZFRkVGZXItRiM2Jy1GLDYlUSRzaW5GJ0Zbc0ZFRl5wRl51Rl1vRkVGZXItRmJxNiUtRkg2LVEvJkV4cG9uZW50aWFsRTtGJ0ZFRktGZW9GUEZSRlRGVkZYRlovRmhuUSwwLjExMTExMTFlbUYnLUYjNiYtRiw2JVEiaUYnRjlGPEZlci1GLDYlUScmIzk2NjtGJ0Zbc0ZFRkVGXnRGRUYrRl1vRkVGK0Zdb0ZFRkVGXW9GRUYrRl1vRkVGK0Zdb0ZFRitGXW9GRQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUkjbW5HRiQ2JFEiM0YnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiYtRkg2LVEqJnVtaW51czA7RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GYW8tRkI2JFEiMUYnRkUvJStleGVjdXRhYmxlR0ZNRkVGK0Zmb0ZFLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkg2LVEjOj1GJ0ZFRktGX29GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GX3AtRiM2Jy1GLDYlUSlzaW1wbGlmeUYnRjlGPC1GSDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZFRktGX29GUEZSRlRGVkZYRlovRmhuRmZuLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GIzYqLUklbXN1cEdGJDYlLUZbcTYkLUkmbWZyYWNHRiQ2KC1GIzYlLUZCNiRRIzIxRidGRUZmb0ZFLUYjNidGKy1GIzYmLUZCNiRRIzY0RidGRS1GSDYtUTEmSW52aXNpYmxlVGltZXM7RidGRUZLRl9vRlBGUkZURlZGWEZaRmlwLUYsNiVRJyYjOTYwO0YnL0Y6Rk1GRUZFRitGZm9GRS8lLmxpbmV0aGlja25lc3NHRmVvLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBzLyUpYmV2ZWxsZWRHRk1GRS1GZ3E2KC1GIzYlRmNvRmZvRkUtRiM2JS1GQjYkUSIyRidGRUZmb0ZFRlxzRl5zRmFzRmNzLyUxc3VwZXJzY3JpcHRzaGlmdEdGam9GZXItRltxNiQtRiM2J0YrLUYjNictRkI2JFEiNUYnRkVGZXItRiM2Jy1GLDYlUSRjb3NGJ0Zbc0ZFRmZwLUZbcTYkLUYjNiUtRiw2JVEnJiM5NTI7RidGW3NGRUZmb0ZFRkVGZm9GRUYrRkUtRkg2LVEoJm1pbnVzO0YnRkVGS0Zfb0ZQRlJGVEZWRlhGYG9GYm9GY29GRUZFRmVyLUYjNictRiw2JVEkc2luRidGW3NGRUZmcEZedUZmb0ZFRmVyLUZicTYlLUZINi1RLyZFeHBvbmVudGlhbEU7RidGRUZLRl9vRlBGUkZURlZGWEZaL0ZoblEsMC4xMTExMTExZW1GJy1GIzYnRlxvLUYjNiYtRiw2JVEiaUYnRjlGPEZlci1GLDYlUScmIzk2NjtGJ0Zbc0ZFRkVGK0Zmb0ZFRl50RkVGK0Zmb0ZFRkVGZm9GRUYrRmZvRkVGK0Zmb0ZFRitGZm9GRQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiM0YnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZCNiRRIjJGJ0ZFLyUrZXhlY3V0YWJsZUdGTUZFLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkg2LVEjOj1GJ0ZFRksvRk9GTUZQRlJGVEZWRlgvRmVuUSwwLjI3Nzc3NzhlbUYnL0ZobkZnby1GIzYnLUYsNiVRKXNpbXBsaWZ5RidGOUY8LUZINi1RMCZBcHBseUZ1bmN0aW9uO0YnRkVGS0Zlb0ZQRlJGVEZWRlhGWi9GaG5GZm4tSShtZmVuY2VkR0YkNiQtRiM2J0YrLUYjNiotSSVtc3VwR0YkNiUtRmNwNiQtSSZtZnJhY0dGJDYoLUYjNiUtRkI2JFEkMTA1RidGRUZdb0ZFLUYjNidGKy1GIzYmLUZCNiRRIzMyRidGRS1GSDYtUTEmSW52aXNpYmxlVGltZXM7RidGRUZLRmVvRlBGUkZURlZGWEZaRmFwLUYsNiVRJyYjOTYwO0YnL0Y6Rk1GRUZFRitGXW9GRS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaXIvJSliZXZlbGxlZEdGTUZFLUZfcTYoLUYjNiUtRkI2JEZmckZFRl1vRkUtRiM2JUZqbkZdb0ZFRmRyRmdyRmpyRlxzLyUxc3VwZXJzY3JpcHRzaGlmdEdGYW9GXXItRiM2JC1GanA2JS1GIzYnLUYsNiVRJHNpbkYnRmNyRkVGXnAtRmNwNiQtRiM2JS1GLDYlUScmIzk1MjtGJ0ZjckZFRl1vRkVGRUZdb0ZFRmpuRmZzRkVGXXItRiM2Jy1GLDYlUSRjb3NGJ0ZjckZFRl5wRmF0Rl1vRkVGXXItRmpwNiUtRkg2LVEvJkV4cG9uZW50aWFsRTtGJ0ZFRktGZW9GUEZSRlRGVkZYRlovRmhuUSwwLjExMTExMTFlbUYnLUYjNihGam5GXXItRiw2JVEiaUYnRjlGPEZdci1GLDYlUScmIzk2NjtGJ0ZjckZFRkVGZnNGRUYrRl1vRkVGRUZdb0ZFRitGXW9GRUYrRl1vRkVGK0Zdb0ZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUkjbW5HRiQ2JFEiM0YnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiYtRkg2LVEqJnVtaW51czA7RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GYW8tRkI2JFEiMkYnRkUvJStleGVjdXRhYmxlR0ZNRkVGK0Zmb0ZFLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkg2LVEjOj1GJ0ZFRktGX29GUEZSRlRGVkZYL0ZlblEsMC4yNzc3Nzc4ZW1GJy9GaG5GX3AtRiM2Jy1GLDYlUSlzaW1wbGlmeUYnRjlGPC1GSDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZFRktGX29GUEZSRlRGVkZYRlovRmhuRmZuLUkobWZlbmNlZEdGJDYkLUYjNidGKy1GIzYqLUklbXN1cEdGJDYlLUZbcTYkLUkmbWZyYWNHRiQ2KC1GIzYlLUZCNiRRJDEwNUYnRkVGZm9GRS1GIzYnRistRiM2Ji1GQjYkUSMzMkYnRkUtRkg2LVExJkludmlzaWJsZVRpbWVzO0YnRkVGS0Zfb0ZQRlJGVEZWRlhGWkZpcC1GLDYlUScmIzk2MDtGJy9GOkZNRkVGRUYrRmZvRkUvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmFzLyUpYmV2ZWxsZWRHRk1GRS1GZ3E2KC1GIzYlLUZCNiRGXnNGRUZmb0ZFLUYjNiVGY29GZm9GRUZcc0Zfc0Zic0Zkcy8lMXN1cGVyc2NyaXB0c2hpZnRHRmpvRmVyLUYjNiQtRmJxNiUtRiM2Jy1GLDYlUSRzaW5GJ0Zbc0ZFRmZwLUZbcTYkLUYjNiUtRiw2JVEnJiM5NTI7RidGW3NGRUZmb0ZFRkVGZm9GRUZjb0ZedEZFRmVyLUYjNictRiw2JVEkY29zRidGW3NGRUZmcEZpdEZmb0ZFRmVyLUZicTYlLUZINi1RLyZFeHBvbmVudGlhbEU7RidGRUZLRl9vRlBGUkZURlZGWEZaL0ZoblEsMC4xMTExMTExZW1GJy1GIzYnRlxvLUYjNihGY29GZXItRiw2JVEiaUYnRjlGPEZlci1GLDYlUScmIzk2NjtGJ0Zbc0ZFRkVGK0Zmb0ZFRl50RkVGK0Zmb0ZFRkVGZm9GRUYrRmZvRkVGK0Zmb0ZFRitGZm9GRQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiM0YnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnRkEvJStleGVjdXRhYmxlR0ZNRkUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GSDYtUSM6PUYnRkVGSy9GT0ZNRlBGUkZURlZGWC9GZW5RLDAuMjc3Nzc3OGVtRicvRmhuRmRvLUYjNictRiw2JVEpc2ltcGxpZnlGJ0Y5RjwtRkg2LVEwJkFwcGx5RnVuY3Rpb247RidGRUZLRmJvRlBGUkZURlZGWEZaL0ZobkZmbi1JKG1mZW5jZWRHRiQ2JC1GIzYnRistRiM2Jy1GSDYtUSomdW1pbnVzMDtGJ0ZFRktGYm9GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GanAtRiM2KC1JJW1zdXBHRiQ2JS1GYHA2JC1JJm1mcmFjR0YkNigtRiM2JS1GQjYkUSMzNUYnRkVGam5GRS1GIzYnRistRiM2Ji1GQjYkUSM2NEYnRkUtRkg2LVExJkludmlzaWJsZVRpbWVzO0YnRkVGS0Zib0ZQRlJGVEZWRlhGWkZecC1GLDYlUScmIzk2MDtGJy9GOkZNRkVGRUYrRmpuRkUvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl5zLyUpYmV2ZWxsZWRHRk1GRS1GZHE2KC1GIzYlLUZCNiRGW3NGRUZqbkZFLUYjNiUtRkI2JFEiMkYnRkVGam5GRUZpckZcc0Zfc0Zhcy8lMXN1cGVyc2NyaXB0c2hpZnRHRl5vRmJyLUYjNiQtRl9xNiUtRiM2Jy1GLDYlUSRzaW5GJ0ZockZFRltwLUZgcDYkLUYjNiUtRiw2JVEnJiM5NTI7RidGaHJGRUZqbkZFRkVGam5GRUZBRl50RkVGYnItRl9xNiUtRkg2LVEvJkV4cG9uZW50aWFsRTtGJ0ZFRktGYm9GUEZSRlRGVkZYRlovRmhuUSwwLjExMTExMTFlbUYnLUYjNihGQUZici1GLDYlUSJpRidGOUY8RmJyLUYsNiVRJyYjOTY2O0YnRmhyRkVGRUZedEZFRitGam5GRUYrRmpuRkVGRUZqbkZFRitGam5GRUYrRmpuRkVGK0ZqbkZFLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUkjbW5HRiQ2JFEiM0YnL0Y9USdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0ZFLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYjNiYtRkg2LVEqJnVtaW51czA7RidGRUZLL0ZPRk1GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GYW9GQS8lK2V4ZWN1dGFibGVHRk1GRUYrRmNvRkUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GSDYtUSM6PUYnRkVGS0Zfb0ZQRlJGVEZWRlgvRmVuUSwwLjI3Nzc3NzhlbUYnL0ZobkZccC1GIzYnLUYsNiVRKXNpbXBsaWZ5RidGOUY8LUZINi1RMCZBcHBseUZ1bmN0aW9uO0YnRkVGS0Zfb0ZQRlJGVEZWRlhGWi9GaG5GZm4tSShtZmVuY2VkR0YkNiQtRiM2J0YrLUYjNigtSSVtc3VwR0YkNiUtRmhwNiQtSSZtZnJhY0dGJDYoLUYjNiUtRkI2JFEjMzVGJ0ZFRmNvRkUtRiM2J0YrLUYjNiYtRkI2JFEjNjRGJ0ZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGX29GUEZSRlRGVkZYRlpGZnAtRiw2JVEnJiM5NjA7RicvRjpGTUZFRkVGK0Zjb0ZFLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zecy8lKWJldmVsbGVkR0ZNRkUtRmRxNigtRiM2JS1GQjYkRltzRkVGY29GRS1GIzYlLUZCNiRRIjJGJ0ZFRmNvRkVGaXJGXHNGX3NGYXMvJTFzdXBlcnNjcmlwdHNoaWZ0R0Znb0Zici1GIzYkLUZfcTYlLUYjNictRiw2JVEkc2luRidGaHJGRUZjcC1GaHA2JC1GIzYlLUYsNiVRJyYjOTUyO0YnRmhyRkVGY29GRUZFRmNvRkVGQUZedEZFRmJyLUZfcTYlLUZINi1RLyZFeHBvbmVudGlhbEU7RidGRUZLRl9vRlBGUkZURlZGWEZaL0ZoblEsMC4xMTExMTExZW1GJy1GIzYnRlxvLUYjNihGQUZici1GLDYlUSJpRidGOUY8RmJyLUYsNiVRJyYjOTY2O0YnRmhyRkVGRUYrRmNvRkVGXnRGRUYrRmNvRkVGRUZjb0ZFRitGY29GRUYrRmNvRkVGK0Zjb0ZFIn this case, as a little sample of a calculation, we can calculate the density of probability of an electron with the following quantum numbers: n = 1, l = 0 and m = 0, around the nucleus. 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 this case, we need to clarify that we are aproximating this calculation near to the nucleus of the atom and therefore we need to evaluate this last expression when R = 0.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As we can see, the result obtained is consistent with the expected result. Another useful application that we can produce with this is the calculation of the 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
<Text-field style="Heading 1" layout="Heading 1">Solution and Graphical Display of the Solution</Text-field>Graphic Solution for 1s 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Graphic Solution for 2s 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Solution for 3s 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<Text-field style="Heading 1" layout="Heading 1">References</Text-field>1 Charles S. Johnson, Lee G. Pedersen, Problems and Solutions in Quantum Chemistry and Physics, Dover Publications, New York, 1986.
2 Hancs C. Ohanian, Modern Physics, 2nd ed., Prentice Hall 1987, 1995.
3 Paul Tipler, Modern Physics, Worth Publishers, 1969, 1978.
4 David Griffiths, Introduction to Electrodynamics, 3rd ed., Prentice Hall, 1981, 1989, 1999.
5 George B. Arfken, Hans J. Weber, Mathematical Methods For Physicists, 5th ed., Harcourt Academic Press 2001, 1995, 1985, 1970, 1966.