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Y_Kistochka [10]
3 years ago
6

What is the wavelength (in nm) of a photon emitted during transition from the n = 3 state to the n = 1 state in the H atom?

Physics
1 answer:
Mkey [24]3 years ago
4 0

Answer:

\lambda=103\ nm

Explanation:

E_n=-2.179\times 10^{-18}\times \frac{1}{n^2}\ Joules

For transitions:

Energy\ Difference,\ \Delta E= E_f-E_i =-2.179\times 10^{-18}(\frac{1}{n_f^2}-\frac{1}{n_i^2})\ J=2.179\times 10^{-18}(\frac{1}{n_i^2} - \dfrac{1}{n_f^2})\ J

\Delta E=2.179\times 10^{-18}(\frac{1}{n_i^2} - \dfrac{1}{n_f^2})\ J

Also, \Delta E=\frac {h\times c}{\lambda}

Where,  

h is Plank's constant having value 6.626\times 10^{-34}\ Js

c is the speed of light having value 3\times 10^8\ m/s

So,  

\frac {h\times c}{\lambda}=2.179\times 10^{-18}(|\frac{1}{n_i^2} - \dfrac{1}{n_f^2}|)\ J

\lambda=\frac {6.626\times 10^{-34}\times 3\times 10^8}{{2.179\times 10^{-18}}\times (|\frac{1}{n_i^2} - \dfrac{1}{n_f^2}|)}\ m

So,  

\lambda=\frac {6.626\times 10^{-34}\times 3\times 10^8}{{2.179\times 10^{-18}}\times (|\frac{1}{n_i^2} - \dfrac{1}{n_f^2}|)}\ m

Given, n_i=3\ and\ n_f=1

\lambda=\frac{6.626\times 10^{-34}\times 3\times 10^8}{{2.179\times 10^{-18}}\times |(\frac{1}{3^2} - \dfrac{1}{1^2})}|\ m

\lambda=\frac{10^{-26}\times \:19.878}{10^{-18}\times \:2.179|\left(\frac{1}{9}-\frac{1}{1}\right)|}\ m

\lambda=1.03\times 10^{-7}\ m

1 m = 10⁻⁹ nm

\lambda=103\ nm

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a) a geostationary satellite is that it is always at the same point with respect to the planet,

b) f = 2.7777 10⁻⁵ Hz

c)                           d)   w = 1.745 10⁻⁴ rad / s

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                 .w = 2pi /t

                  w = 2pi / 3.6 10⁴

                  w = 1.745 10⁻⁴ rad / s

how fast is

                  v = w r

                  v = 1.75 10-4 (69.911 106 + 120 106)

                  v = 190017 m / s

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