Question

When an electron makes a transition from (n + 1) state to n state, the frequency of emitted radiations is related to n according to (n>> 1) :

• A. v $\alpha$ n${}^{-3}$
• B. v $\alpha$ n${}^2$
• C. v $\alpha$ n${}^3$
• D. v $\alpha$ n${}^{\frac{2}{3}}$

Answer 1

Answer: (A)

v $\alpha$ n${}^{-3}$

$\Delta E=h\upsilon =-R_H(\frac{1}{{n_f}^2}-\frac{1}{{n_i}^2})$

$n_f$ - the final energy level

$n_i$ - the initial energy level

$R_H$ - Rydberg's constant, expressed in joules. The constant value is $2.18X{10}^{-18}J$

$v\propto \{\frac{1}{(n-1{)}^2}-\frac{1}{n^2}\}⟹v\propto \frac{(2n-1)}{n^2(n-1{)}^2}⟹v\propto \frac{1}{n^3}$

Hence, answer is A.