Question

Q1:What is the separation between double slits that produces a second order minimum at 37.5

Answer 1

kinetic energy of proton = KE = 2 keV = 2 x 10³ x 1.6 x 10^-19 J = 3.2 x 10^-16 J          (since 1 eV = 1.6 x 10^-19 J )

Kinetic energy is given as ::
KE = (0.5) m V²

3.2 x 10^-16 = (0.5) (1.67 x 10^-27) V²             m = mass of proton = 1.67 x 10^-27 kg

V = 6.2 x 10⁵ m/s

Using the debrogli'e principle , the wavelength can be calculated as \

= h/mV

= (6.63 x 10^-34) / (1.67 x 10^-27 x 6.2 x 10⁵)

= 0.6403 x 10^-12 m

Using the formula for second order minima

d sin = (n + 1/2)

d = slit width

n= 2

d sin37.5 = (2 + 1/2) (0.6403 x 10^-12 )

d = 2.63 x 10^-12 m