Question

Calculate energy in kcal/mole necessary to remove an electron in a hydrogen atom in fourth principal quantum number to infinity.

Answer 1

We know Rydberg's equation

$\frac{1}{\lambda }=R{Z}^2[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$

remove an electron from $4^{th}$ quantum no to $\infty$

$\Rightarrow n_1=4,n_2=\infty$

hydrogen atom$\Rightarrow z=1$

$\frac{1}{\lambda }=R{\left(1\right)}^2[\frac{1}{4^2}-\frac{1}{{\infty }^2}]$

$\frac{1}{\lambda }=\frac{R}{4^2}$

$\lambda =\frac{16}{R}=\frac{16}{10967800}$

$\lambda =14.59\times {10}^{-7}m$

$E=\frac{hc}{\lambda }$

$E=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{14.59\times {10}^{-7}}$

$E=1.36\times {10}^{-19}joules$

$E=1.36\times {10}^{-19}\frac{1}{4.18}\times {10}^{-3}\frac{kcal}{mol}\times 6.023\times {10}^{23}$

$=19.634\frac{kcal}{mol}$

energy required is $19.634kcal/mol.$