Question

What must be the velocity of a beam of electrons if they are to display a deBroglie wavelength of 100Å

Answer 1

Use De- broglie's wavelength formula,
e.g., λ = h/mv
Here λ is the wavelength of Particle
v is the speed of particle and m is the mass of Particle.

Here, λ = 100 A° = 10⁻⁸ m
m = 9.1 × 10⁻³¹ Kg [ mass of electron ]
h = 6.626 × 10⁻³⁴ J.S

Now, 10⁻⁸ = 6.626 × 10⁻³⁴/(9.1 × 10⁻³¹ × v)
v = 6.626 × 10⁻³/(9.1 × 10⁻⁸)
= 0.7281 × 10⁵ m/s
= 7.281 × 10⁴ m/s

Hence, velocity of electron = 7.281 × 10⁴ m/s

Answer 2

Given conditions ⇒

De-Broglie wavelength of the Electrons = 100 Angstrom.
 = 100 × 10⁻¹⁰ m.
 = 10⁻⁸ m.

Using the Formula,
 λ = h/p

where, h is the plank constant = 6.63 × 10⁻³⁴ J-s.
p is the momentum.
 p = mv
 p = 9.1 × 10⁻³¹ × v.

∴ 10⁻⁸ = (6.63 × 10⁻³⁴) ÷ (9.1 × 10⁻³¹ × v)
⇒  v = (6.63 × 10⁻³ × 10⁸) ÷ 9.1
⇒ v = 0.728 × 10⁵
∴ v = 7.28 × 10⁴ m/s.


Hence, the Velocity of the Electrons is 7.28 × 10⁴ m/s.



Hope it helps.