Two electrons are moving with different kinetic energies. If 1st electron is moving with kinetic energy k and the 2nd electron with kinetic energy 4k, the ratio of their de Broglie wavelengths will be respectively:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 : 1
De-Broglie Wavelength (λ) can be expressed as -
$λ=\frac{h}{\sqrt{2m_eK.E.}}$
where,
$m_e$ = Mass of electron
$K.E.$ = Kinetic Energy
Kinetic energy of 1st electron $(K_1)=K$
Kinetic energy of 2nd electron $(K_2)=4K$
$∴λ_1=\frac{h}{\sqrt{2m_eK}},λ_2=\frac{h}{\sqrt{2m_e4K}}$
$∴\frac{λ_1}{λ_2}=\frac{\frac{h}{\sqrt{2m_eK}}}{\frac{h}{2\sqrt{2m_eK}}}=\frac{2}{1}$