Verified Solution • 2025–26 Session moderate

QJEEM20Ph9418: JEE Main 2020 Physics - Class 12 JEEM20Ph9418 Solution: A particle is moving 5 times as fast as an electron. The ratio…

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 ×\times 10–4. The mass of the particle is close to

Multiple Choice Options

  • A 1.2 ×\times 10–28 kg
  • B 9.1 ×\times 10–31 kg
  • C 4.8 ×\times 10–27 kg
  • D 9.7 ×\times 10–28 kg

Step-by-Step Verified Solution

Let mass of particle = m

Let speed of e– = V

∴\therefore speed of particle = 5V

de-broglie wavelength λ\lambda d = hP=hmv{h \over P} = {h \over {mv}}

∴\therefore ( λ\lambda d)P = hm(5V){h \over {m\left( {5V} \right)}} ....(1)

and ( λ\lambda d)e = hme(V){h \over {{m_e}\left( V \right)}} ....(1)

According to question

(λd)P(λd)e=me5m{{{{\left( {{\lambda _d}} \right)}_P}} \over {{{\left( {{\lambda _d}} \right)}_e}}} = {{{m_e}} \over {5m}} = 1.878 ×\times 10–4

⇒\Rightarrow m = me5×1.874×10−4{{{m_e}} \over {5 \times 1.874 \times {{10}^{ - 4}}}}

= 9.1×10−315×1.874×10−4{{9.1 \times {{10}^{ - 31}}} \over {5 \times 1.874 \times {{10}^{ - 4}}}}

= 9.7 ×\times 10–28 kg

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