A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

Question

Choose correct option :
(A) Number of photons required for a light beam of 2000 pm wavelength and 1 Joule energy is \(1.01 \times 10^{16}\).
(B) Light with wavelength 300 nm has energy \(E_1\) and for wavelength 900 nm has energy \(E_2\), then \(E_1/E_2 = 1/3\).
(C) Frequency of light is \(4.5 \times 10^{16}\) Hz then its wavelength is \(6.7 \times 10^{-9}\) m.
(D) If electrons and protons are accelerated by same potential difference, then their de-Broglie wavelength are equal.

Answer 1

Given:

Velocity of particle = 4 × velocity of electron
v_p = 4v_e

Ratio of de-Broglie wavelengths:
λ_p : λ_e = 2 : 1

Step 1: Write de-Broglie wavelength formula

λ = h / mv

Step 2: Take ratio of wavelengths

λ_p / λ_e = (h / m_pv_p) / (h / m_ev_e)

λ_p / λ_e = (m_ev_e) / (m_pv_p)

Given λ_p / λ_e = 2

(m_ev_e) / (m_pv_p) = 2

Step 3: Substitute v_p = 4v_e

(m_ev_e) / (m_p · 4v_e) = 2

m_e / (4m_p) = 2

Step 4: Solve for m_p

m_e = 8m_p

m_p = m_e / 8

Final Answer:

The mass of the particle is,
1/8 times the mass of the electron

A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

Show Hint

The Correct Option is D

Solution and Explanation

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