Question

The frequency of resulting spectral line, in cycle per seconds is:

• A. $1.93\times {10}^{-11}$
• B. $2.9\times {10}^{16}$
• C. $1.93\times {10}^{11}$
• D. $2.9\times {10}^{-11}$

Answer 1

The correct option is B $2.9\times {10}^{16}$

We know that during transition of electron energy is released, this energy is emitted in the form of photon which is given by,

$E=\frac{13.6}{n^2}eV$ for an hydrogen atom

During transition from $n_1=3$ the $n_2=1$

$E=13.60(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2})eV$

$E=12.1eV=1.936\times {10}^{-18}J$

$E=h\nu$

$\nu =\frac{E}{h}Hz$

$\nu =\frac{1.936\times {10}^{-18}J}{6.63\times {10}^{-34}Js}$

$\nu =2.9\times {10}^{16}Hz$