Question

Calculate the velocity and kinetic energy with which the electrons strike the target of an x-ray tube operated at 50000 volts.what is the short wavelength

Answer 1

Kinetic energy = charge × potential difference
Here , charge on electron = 1.6 × 10⁻¹⁸C
Potential difference = 50,000 volts
So, Kinetic energy = 1.6 × 10⁻¹⁹C × 50,000 volts = 8 × 10⁻¹⁵ J

We know,
Kinetic energy = 1/2mv²
8 × 10⁻¹⁵ = 1/2 × 9.1 × 10⁻³¹ × v² [ ∵ m is the mass of electron , e.g., 9.1 × 10⁻³¹ Kg]
v² = 16/9.1× 10¹⁶
v ≈ 1.3 × 10⁸ m/s
Hence, velocity of striking electron strike the target is 1.3 × 10⁸ m/s

Now, wavelength = λ
hc/λ = kinetic energy
1/λ = 8 × 10⁻¹⁵/6.626 × 10⁻³⁴ × 3 × 10⁸
λ = 6.626 × 3 × 10⁻²⁶/8 × 10⁻¹⁵ = 0.248 × 10⁻¹⁰ m
hence, wavelength is 0.248A°