Question

The quantum mechanical treatment of the hydrogen atom gives the energy value:
i) use this expression to find ΔE between n = 3 and m=4
ii) Calculate the wavelength corresponding to the above transition.

Answer 1

^_^ ATOMIC STRUCTURE •_^

Final Answer :i) Del(E) = 0.66eV/atom
ii) 18.07 * 10^(-7) m

Steps:
1) Del(E) = E(4) - E(3)

$= \frac{ - 13.6}{ {4}^{2} } - \frac{ - 13.6}{ {3}^{2} } \\ = 13.6 \times ( \frac{1}{ {3}^{2} } - \frac{1}{ {4}^{2} } ) \\ = 0.66 \: ev \: \div atom$

2) Now, We will change units of del(E) to SI units.
Then, equate it to Energy of Photon.

del(E) = hc/lambda
=>
$= > 0.66 \times 1.6 \times {10}^{ - 19} = \frac{6.626 \times {10}^{ - 34} \times 3 \times {10}^{8} }{ \lambda} \\ = > \lambda = \frac{6.626 \times 3 \times {10}^{ - 7} }{0.66 \times 1.6} \\ = > \lambda = 18.82 \times {10}^{ - 7} \: m$

Hence, Wavelength of trasition photon is 18.82 * 10^(-7) m