Which of the following has the longest de-Broglie wavelength if they are moving with same velocity ?

Question

Which of the following has the longest de-Broglie wavelength if they are moving with same velocity ? (A) Neutron (B) Proton (C) α-particle (D) β-particle

Tardigrade Admin · Accepted Answer

According to de-Broglie hypothesis, the wavelength of the wave associated with particle moving with velocity v is given by

λ = \frac{h}{m v}

Since, v remains the same, therefore

λ \propto \frac{1}{m}

As

m_{α} > m_{n} > m_{p} > m_{β}

∴ λ_{α} < λ_{n} < λ_{p} < λ_{β}

Therefore,

β

particle has longest wavelength.

Q. Which of the following has the longest de-Broglie wavelength if they are moving with same velocity ?

Neutron

Proton

$α$ -particle

$β$ -particle

Q. Which of the following has the longest de-Broglie wavelength if they are moving with same velocity ?

Neutron

Proton

α-particle

β-particle

According to de-Broglie hypothesis, the wavelength of the wave associated with particle moving with velocity v is given by λ=mvh​ Since, v remains the same, therefore λ∝m1​ As mα​>mn​>mp​>mβ​ ∴λα​<λn​<λp​<λβ​ Therefore, β particle has longest wavelength.

$α$ -particle

$β$ -particle