JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Modern Physics

A particle

A

of mass '

m

' and charge '

q

' is accelerated by a potential difference of 50 V . Another particle B of mass ' 4 m ' and charge ' q ' is accelerated by a potential difference of 2500 V . The ratio of de-Broglie wavelength

\frac{λ _{A}}{λ _{B}}

is close to:

(A)10.00
(B)0.07
(C)14.14✓ Correct
(D)4.47

Answer: (C)

Solution

The de Broglie wavelength of a particle accelerated through a potential

V

λ = \frac{h}{2 m q V}

. Both particles carry the same charge

q

, so

λ \propto \frac{1}{mV}

. Particle

A

has mass

m

with

V = 50 V

, while

B

has mass

4 m

with

V = 2500 V

, so

\frac{λ _{A}}{λ _{B}} = \frac{4 m \times 2500}{m \times 50} = 200 = 102 \approx 14.14

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option

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