An incident light is monochromatic and of wavelenght 600nm, the kinetic energy of the electron is 2.56 x 10^(-20)J. For light of wavelenght 400nm, it is 1.92 x 10^(-19)J.
Use the above information to estimate the value of Planck's constant,h and the work function,W of the metal.
(Take the velocity of light to be 3 x 10^98)m/s)
To estimate the value of Planck's constant (h) and the work function (W) of the metal, we can use the Einstein's photoelectric equation:
E = hf - W
where E is the kinetic energy of the electron, h is Planck's constant, f is the frequency of the incident light, and W is the work function of the metal.
First, let's find the frequencies of the two monochromatic lights using the formula:
f = c / λ
where c is the velocity of light (3 x 10^8 m/s) and λ is the wavelength.
For the light with a wavelength of 600 nm:
f1 = (3 x 10^8 m/s) / (600 x 10^(-9) m)
= 5 x 10^14 Hz
For the light with a wavelength of 400 nm:
f2 = (3 x 10^8 m/s) / (400 x 10^(-9) m)
= 7.5 x 10^14 Hz
Now, let's use the given kinetic energy values to create two equations:
2.56 x 10^(-20) J = h * (5 x 10^14 Hz) - W
1.92 x 10^(-19) J = h * (7.5 x 10^14 Hz) - W
We have two equations and two unknowns (h and W). To solve this system of equations, we can rearrange them to isolate h and W:
h = (E + W) / f
First, let's solve for h in terms of the first equation:
h1 = (2.56 x 10^(-20) J + W) / (5 x 10^14 Hz)
Next, let's solve for h in terms of the second equation:
h2 = (1.92 x 10^(-19) J + W) / (7.5 x 10^14 Hz)
Now, let's equate h1 and h2 to find a common value for h:
(2.56 x 10^(-20) J + W) / (5 x 10^14 Hz) = (1.92 x 10^(-19) J + W) / (7.5 x 10^14 Hz)
Cross-multiplying, we get:
(2.56 x 10^(-20) J + W) * (7.5 x 10^14 Hz) = (1.92 x 10^(-19) J + W) * (5 x 10^14 Hz)
Expanding the equation:
(19.2 x 10^(-20) J + 7.5W) = (9.6 x 10^(-19) J + 5W)
Simplifying the equation:
12.2 x 10^(-20) J = 2.5W
W = (12.2 x 10^(-20) J) / 2.5
W ≈ 4.88 x 10^(-20) J
Now, let's substitute the value of W into any of the initial equations to find h. Let's use the first equation:
2.56 x 10^(-20) J = h * (5 x 10^14 Hz) - 4.88 x 10^(-20) J
Rearranging the equation to isolate h:
h ≈ (2.56 x 10^(-20) J + 4.88 x 10^(-20) J) / (5 x 10^14 Hz)
h ≈ 7.44 x 10^(-20) J / (5 x 10^14 Hz)
h ≈ 1.488 x 10^(-34) J·s
Therefore, the estimated value of Planck's constant (h) is approximately 1.488 x 10^(-34) J·s and the work function (W) of the metal is approximately 4.88 x 10^(-20) J.