Question

Find the de Broglie wavelength (in m) of an electron moving in the second Bohr orbit of hydrogen.

• A. $3.34\times {10}^{-10}$
• B. $4.68\times {10}^{-10}$
• C. $5.67\times {10}^{-10}$
• D. $6.67\times {10}^{-10}$

Answer 1

The correct option is D $6.67\times {10}^{-10}$

We know,
Velocity of an electron in Bohr's orbit is given by,
$v=\frac{2.18\times {10}^6\times Z}{n}m/sec$

So, velocity of an electron in Bohr's second orbit of hydrogen is,
$v=1.09\times {10}^{6}m/sec$

Again,we know,
$\text{Mass of electron}\left(m_e\right)=9.1\times {10}^{-31}kg\text{Planck's constant}\left(h\right)=6.62\times {10}^{-34}Js$
$\text{de Broglie wavelength}\left(\lambda \right)=\frac{h}{mv}=\frac{6.62\times {10}^{-34}}{9.1\times {10}^{-31}\times 1.09\times {10}^6}=6.67\times {10}^{-10}m$