physics

Question

1 Light of frequency 5.2 x 10^14 Hz is incident on a pair of straight parallel slits where the slits

are 0.17 mm apart. It creates an interference pattern on a screen 7.8 m away. What is the

distance from the centre of the pattern to the fourth bright line?

 

2. What is the maximum wavelength of radiation that causes photoelectric emission from a

surface whose work function is 5.4 eV?

 

3. An x-ray collides with a stationary electron. What is the change in the wavelength of an xray

if it is scattered through an angle of 125 degrees? 

Answer 1

(1)

Frequency of light is f = 5.2  x 10^14 Hz .

The Distance between two slits d is 0.17 mm = 0.17 * 10^-3 m

Distance between screen and slit L is 7.8 m

Fourth order bright line ⇒ Fourth order antinodal point ⇒ m = 4 .

Young's Equation is λ = ( y * d) / (m * L)

Where y is distance between fourth bright line and central antinode .

y = [ λ x (m * L) ] / d 

y = [ c x (m * L) ] / ( f * d )      [ Since λ = c / f ]

y = [ 3 x 10⁸ (4 * 7.8) ] / ( 5.2x 10¹⁴ * 0.17 x 10^-3 )  

y = 0.10588 ⇒ 10.588 x 10^-2 m

Distance between fourth bright line and central antinode is  10.588 cm

Answer 2

(2)

Work function of a photoelectric surface w = 5.4 eV = 8.65175 x 10^-19 J .

Work function of a photoelectric surface w = h * f₀ ⇒ (h * c) / λ .      [Since f₀ = c / λ ]

Where h is plank's constant = 6.63 × 10^-34 J·sec .

         c = velocity of light = 3 × 10⁸ m/s .

 λ =  (h * c) / w

 λ = (6.63 × 10^-34  × 3 × 10⁸ )/ 8.65175 x 10^-19

 λ = 2.2975 × 10^-7 m

 λ = 229.75  nm .

The maximum wave length of the λ = 229.75  nm .

Answer 3

(3)

Scattered  angle is 125° .

Change in the wavelength of an xray after scattered is

 

Where h is plank's constant = 6.63 × 10^-34 J·sec .

         c = velocity of light = 3 × 10⁸ m/s .

         m_e is the electron rest mass = 9.11 × 10^-31 kg .

The value of Compton wavelength (h/m_ec) = 2.42 × 10^-12 

Change in wave length is = (2.42 × 10^-12 )(1- cos 125)

                                          = (2.42 × 10^-12 )(1.5735)

                                          = 3.8080 × 10^-12 

Change in wave length is 3.8080 pm .