Question

1. X-rays are scattered from a target at an angle of 35.4° with the direction of the incident beam. Find the wavelength shift of the scattered x-rays.

nm

2. (a) If the wavelength of an electron is 4.61 ✕ 10⁻⁷ m, how fast is it moving?
km/s

(b) If the electron has a speed equal to 8.30 ✕ 10⁶ m/s, what is its wavelength?
m

Answer 1

1 )

given

= 35.4°

the wavelength shift of the scattered x-rays = = ?

using equation,

= ( h / m_e C ) ( 1 - cos )

= ( 6.627 x 10^-34 / 9.1 x 10^-31 x 3 x 10⁸ ) (1 - cos35.4 )

= 4.4877 x 10^-13 m

= 0.00044877 x 10^-9 m

= 0.00044877 nm

the wavelength shift of the scattered x-rays is = 0.00044877 nm

2 )

a )

given

the wavelength of an electron is 4.61 x 10⁻⁷ m =

speed V = ?

using equation = h / m V

4.61 x 10⁻⁷ = 6.627 x 10^-34 / 9.1 x 10^-31 x V

V = 6.627 x 10^-34 / 9.1 x 10^-31 x 4.61 x 10⁻⁷

V = 1579.7 m/sec

or

V = 1.5797 km/sec

it moving with a speed of V = 1.5797 km/sec

b )

given

speed equal to 8.30 x 10⁶ m/s = V

=?

using equation = h / m V

= 6.627 x 10^-34 / 9.1 x 10^-31 x 8.30 x 10⁶

= 8.77399 x 10^-11 m

or

= 0.0877399 x 10^-9 m

= 0.0877399 nm  

its wavelength is = 0.0877399 nm