Question

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

• A. $3.34\times {10}^{-10}$
• B. $8.34\times {10}^{-9}$
• C. $5.34\times {10}^{-10}$
• D. $6.34\times {10}^{-9}$

Answer 1

The correct option is A $3.34\times {10}^{-10}$

We know that
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 first orbit of hydrogen is:
$v=2.18\times {10}^{6}m/sec$
We know that:
$\text{Mass of electron}\left(m_e\right)=9.1\times {10}^{-31}kgh=6.63\times {10}^{-34}Js$
$\text{de Broglie wavelength}\left(\lambda \right)=\frac{h}{mv}=\frac{6.63\times {10}^{-34}}{9.1\times {10}^{-31}\times 2.18\times {10}^6}=3.34\times {10}^{-10}m$