Which of the following statement is incorrect in Bohr’s model if the mass of an electron becomes 10 times its original mass ?

# Which of the following statement is incorrect in Bohr’s model if the mass of an electron becomes 10 times its original mass ?

1. A

Velocity of the electron increases by 10 times

2. B

Orbit radius decreases by 10 times

3. C

Energy of electron increases by 10 times

4. D

Wave length of the electron will remain same

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### Solution:

Expression of velocity is, $\mathrm{v}=\frac{2{\mathrm{\pi ze}}^{2}}{\mathrm{nh}}$. As velocity of electron is independent from mass of electron, hence option 1 is wrong.

Expression of radius is, $\mathrm{r}=\frac{{\mathrm{n}}^{2}{\mathrm{h}}^{2}}{4{\mathrm{\pi }}^{2}{\mathrm{mZe}}^{2}}$. If mass increased by 10 times, radius decreases by 10 times. hence, option-2 is correct.

Expression of energy is, $\mathrm{E}=\frac{-2{\mathrm{\pi }}^{2}{\mathrm{mZ}}^{2}{\mathrm{e}}^{4}}{{\mathrm{n}}^{2}{\mathrm{h}}^{2}}$. If mass increases by 10 times, then energy also increases by 10 times. Hence, option-3 is also correct.

Expression of wavelength is, $\mathrm{\lambda }=\frac{2{\mathrm{\pi r}}_{\mathrm{n}}}{\mathrm{n}}$.No dependency on mass, therefore wavelength remains the same. Hence, option-4 is also correct.

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