Question

An electron in the hydrogen atom is excited from $1^{st}$ orbit to $5^{th}$ orbit. The frequency of radiation is:

• A. $0.44\times {10}^{-9}Hz$
• B. $3.15\times {10}^{15}Hz$
• C. $6.2\times {10}^{8}Hz$
• D. $1.13\times {10}^{-12}Hz$

Answer 1

The correct option is B $3.15\times {10}^{15}Hz$

$E=-R_H\times \frac{Z^2}{n^2}$

Where, $R_H$ = Redberg constant

$Z$ = Atomic number of hydrogen

n = number of energy state

For hydrogen atom, Z=1

$E=-2.18\times {10}^{-18}J\times \frac{1}{n^2}$

$△E=E_5-E_1=\frac{-2.18\times {10}^{-18}}{25}-\left(\frac{-2.18\times {10}^{-18}}{1}\right)$

$=\frac{24}{25}\times 2.18\times {10}^{-18}J$

$△E=h\nu \Rightarrow \nu =\frac{△E}{h}=3.15\times {10}^{15}㎐(\because h=6.626\times {10}^{34})$
Hence, the correct option is B.