The wavelength associated with the electron moving in the first orbit of hydrogen atom with velocity $2.2…

The wavelength associated with the electron moving in the first orbit of hydrogen atom with velocity $2.2 \times 10^6 \mathrm{~ms}^{-1}$ (in nm) is $\left(m_e=9.0 \times 10^{-31} \mathrm{~kg}, h=6.6 \times 10^{-34} \mathrm{Js}\right)$
  1. $0.66$
  2. $0.33$
  3. $0.22$
  4. $0.44$

Solution

According to de-Broglie's equation, $\lambda=\frac{h}{m v}$ where, $\lambda$ is wavelength $h$ is Planck's constant $\left(6.626 \times 10^{-34} \mathrm{Js}\right)$ $m$ is mass of electron (given $9.0 \times 10^{-31} \mathrm{~kg}$ ) $v$ is velocity of electron (given $2.2 \times 10^6 \mathrm{~m} / \mathrm{s}$ ) $\therefore \quad \lambda=\frac{6.626 \times 10^{-34}}{9.0 \times 10^{-31} \times 2.2 \times 10^6}$ $=0.33 \times 10^{-9} \mathrm{~m}$ i.e. $0.33 \mathrm{~nm}$ (as $1 \mathrm{~nm}=10^{-9} \mathrm{~m}$ )

Asked in: AP EAMCET 2022 (05 Jul Shift 1)

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