Question

In a photoelectric experiment in which monochromatic light and sodium cathode are used ,we find a stopping potential of 1.8V for l =300/Angstrom and 0.82V for l =4000angstrom form these data determine
A. Value of Plank's constant
B.work function of sodium light in EV
C. threshold wavelength for sodium

Answer 1

We know that the stopping potential is given by the formula:

V_stop = (hc/e) x (1/λ) - (W/e)

where h is Plank's constant, c is the speed of light, e is the charge of an electron, λ is the wavelength of the incident light, and W is the work function of the metal (in electron volts).

Let's use this formula for both wavelengths and the corresponding stopping potentials:

For λ = 300 Å, V_stop = 1.8 V
For λ = 4000 Å, V_stop = 0.82 V

We can write two equations for these data:

1.8 = (hc/e) x (1/300) - (W/e)
0.82 = (hc/e) x (1/4000) - (W/e)

We can solve these equations simultaneously to find the values of Plank's constant (h) and the work function (W):

Multiplying the first equation by 4/3, we get:

2.4 = (hc/e) x (4/900) - (W/e)

Subtracting the second equation from this, we get:

1.58 = (hc/e) x (4/900 - 1/16000)

Simplifying this:

1.58 = (hc/e) x (643/720000)

hc = (1.58 x 720000 x e)/643
h = [(1.58 x 720000 x 1.602 x 10^-19)/(643 x 3 x 10^8)] Joule-seconds
h = 6.626 x 10^-34 Joule-seconds (approximately)

Now, we can use either of the two equations to find the work function. Let's use the first one:

1.8 = (6.626 x 10^-34 x 3 x 10^8)/(1.602 x 10^-19) x (1/300) - (W/e)

Solving for W:

W = (6.626 x 10^-34 x 3 x 10^8 x 1.602 x 10^-19)/e x (1/300) - 1.8
W = 2.28 electron volts (approximately)

Finally, we can use the second equation to find the threshold wavelength, which is the minimum wavelength needed to eject electrons from the cathode (i.e., when V_stop = 0):

0 = (hc/e) x (1/λ_t) - (W/e)

Solving for λ_t:

λ_t = hc/We
λ_t = (6.626 x 10^-34 x 3 x 10^8)/(2.28 x 1.602 x 10^-19) Å
λ_t = 2824.7 Å (approximately)

Therefore, the threshold wavelength for sodium is approximately 2824.7 Å.