Question

The energy required to transfer an electron from second Bohr orbit to third Bohr orbit in a hydrogen like atom with nuclear charge $Z_e$ is $6.8eV$.

The wavelength of radiation required to shift the electron from first orbit to infinite orbit will be :

• A. $2.527A^o$
• B. $25.27A^o$
• C. $252.7A^o$
• D. $2527A^o$

Answer 1

Answer: (B)

$25.27A^o$

For a Hydrogen like species, the energy of each orbit is expressed by the Bohr's model as $E=-\frac{E_0}{n^2}$

Here, $-E_0$ is the energy of the first orbit.

Given that $E\left(3\right)-E\left(2\right)=6.8\text{eV}$

Thus, $E_0(-\frac{1}{9}+\frac{1}{4})=6.8\Rightarrow E_0=48.96\text{eV}$

Hence, in order to shift electron from first orbit to infinity, energy required is $E=48.96\text{eV}$

Wavelength is given by $\lambda =\frac{hc}{E}=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{48.96\times 1.602\times {10}^{-18}}\approx 0.252\times {10}^{-8}\text{m}=25.27A^{\circ }$