What should be the velocity of an electron so that its momentum becomes equal to that of a photon of wavelength 5200 mathringA ?

Question

What should be the velocity of an electron so that its momentum becomes equal to that of a photon of wavelength 5200 mathringA ? (A) 700 ms - 1  (B) 1000 ms - 1  (C) 1400 ms - 1  (D) 2800 ms - 1

Tardigrade Admin · Accepted Answer

Momentum, p = mv = ( h / λ) v = ( h / m λ) ∴ v = ( 6.62 × 10 - 34/ 9.1 × 10 - 31 × 5.2 × 10 - 7 ) ⇒ v = ( 6.62 × 104 / 9.1 × 5.2 ) ⇒ v = 1.4 × 103 ms - 1 ⇒ v = 1400 ms - 1

Q. What should be the velocity of an electron so that its momentum becomes equal to that of a photon of wavelength 5200 $\overset{˚}{A}$ ?

700 $m s^{- 1}$

1000 $m s^{- 1}$

1400 $m s^{- 1}$

2800 $m s^{- 1}$

Momentum, p = mv = $\frac{h}{λ}$
$v = \frac{h}{mλ}$
$∴ v = \frac{6.62 \times 1 0 ^{- 34}}{9.1 \times 1 0 ^{- 31} \times 5.2 \times 1 0 ^{- 7}}$
$\Rightarrow v = \frac{6.62 \times 1 0 ^{4}}{9.1 \times 5.2}$
$\Rightarrow v = 1.4 \times 1 0^{3} m s^{- 1}$
$\Rightarrow v = 1400 m s^{- 1}$

Q. What should be the velocity of an electron so that its momentum becomes equal to that of a photon of wavelength 5200 A˚?

700 ms−1

1000 ms−1

1400 ms−1

2800 ms−1