Question

Calculate the minimum frequency required to remove a first shell electron completely from a hydrogen atom. Given: R $=1.097\times {10}^{-2}$ nm${}^{-1}$

• A. $3.29\times {10}^{15}{s}^{-1}$
• B. $1.30\times {10}^{15}{s}^{-1}$
• C. $2.93\times {10}^{15}{s}^{-1}$
• D. $1.93\times {10}^{15}{s}^{-1}$

Answer 1

The correct option is A $3.29\times {10}^{15}{s}^{-1}$

$n_1=1,n_2=\infty ,R=1.097\times {10}^{-2}n{m}^{-1}\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})=R\left(\frac{1}{1}\right)=1.097\times {10}^7{m}^{-1}So,\lambda =\frac{1}{1.097\times {10}^7}=0.912\times {10}^{-7}m$
So, frequency $\left(\nu \right)=\frac{c}{\lambda }=\frac{3\times {10}^8}{0.912\times {10}^{-7}}=3.29\times {10}^{15}{s}^{-1}$