Question

What wavelength does a neutron (mass = 1.67 × mc021-1.jpg g) moving at 10% of the speed of light have?

Answer 1

By the law of dual nature of particle

E= mc² Given by Einstein ---(1)

E= hc/ lamda given by Plank. -- equation (2)

Combining both equation (1) & (2) we get

mc² = hc/lamda

mc = h/lamda

Lamda = h/mc. ---- equation (3)

Equation 3 is also known as Debroglie's relation between between wave length and velocity.

Where E =energy

M = mass of neutron

c = speed of light

h = Plank's contant

Lamda = wavelength of particle

Putting value of

h = 6.63×10^-34 j/s

c = 3 × 10⁸ m/s

m = 1.6749 × 10^-30 g

Lamda = 6.63 × 10^-34/ 3×10⁷× 1.6749 ×10^-30

Where c= 3× 10⁸×10/100 = 3× 10⁷

lamda = 1.32 × 10^-11 m.