If the de Broglie wavelengths associated with a proton and an α -particle are equal, then the ratio of velocities of the proton and the α -particle will be:

Correct answer: C. 4: 1 According to question, λ_p=λ_α Using, λ=(h)/(p)=(h)/(m v) aligned & So, (h)/(m_p × v_p)=(h)/(m_α × v_α) & (v_p)/(v_α)=(m_α)/(m_p)=(4 m_p)/(m_p) aligned ( of α -particle is 4 times of mass of proton) So, (v_p)/(v_α)=(4)/(1) ; i.e., 4: 1

JEE Main 201815 AprilEvening ShiftOnline

Exam: JEE Main
Year: 2018
Date: 15 April
Shift: Evening Shift
Mode: Online
Subject: Physics
Chapter: Dual Nature of Matter

JEE Main 2018 · 15 April · Evening Shift · Online · Physics · Dual Nature of Matter

If the de Broglie wavelengths associated with a proton and an α...

If the de Broglie wavelengths associated with a proton and an

\alpha

-particle are equal, then the ratio of velocities of the proton and the

\alpha

-particle will be:

Options

A $1: 4$
B $1: 2$
C $4: 1$
D $2: 1$

Correct answer

C. $4: 1$

Step-by-step solution

According to question,

\lambda_p=\lambda_\alpha

Using,

\lambda=\frac{h}{p}=\frac{h}{m v}

\begin{aligned} &\text{ So, } \frac{h}{m_p \times v_p}=\frac{h}{m_\alpha \times v_\alpha} \\ &\Rightarrow \frac{v_p}{v_\alpha}=\frac{m_\alpha}{m_p}=\frac{4 m_p}{m_p} \end{aligned}

(\becausemass of

\alpha

-particle is 4 times of mass of proton) So,

\frac{v_p}{v_\alpha}=\frac{4}{1}

; i.e.,

4: 1

Practice Dual Nature of Matter on Quantrex Academy →

More from Dual Nature of Matter

K_1 and K_2 be the maximum kinetic energies of photoelectrons emitted from a surface of a… JEE Main 2026 The de Broglie wavelength for an electron accelerated through the potential difference of… JEE Main 2026 Given below are two statements: one is labelled as Assertion (A) and the other is… JEE Main 2026 An electron is travelling with a velocity v in free space and when it enters a medium… JEE Main 2026 An electron of mass m is moving in an electric field E = -2E_0 i ( E_0 = constant > 0 )… JEE Main 2026 Light source having wavelength 331 nm is used to generate photo-electrons whose stopping… JEE Main 2026 Match the LIST-I with LIST-II List-I List-II A. Planck's constant I. ML^2T^ -2 B.… JEE Main 2026 The de Broglie wavelength associated with an electron accelerated through a potential… JEE Main 2026 Full Dual Nature of Matter list All JEE Main PYQs