A photoelectric experiment in which monochromatic light and the sodium cathode are used, we find a stopping potential of 1.85 volt for wavelength x=3000anstrong for 0.82 volts, x=4000anstrong. From the data: (a) determine the value of the planck constant. (b) the work function of sodium in the electron volt. (c) the threshold wavelength of sodium.
To determine the value of the Planck constant, work function of sodium, and threshold wavelength of sodium, we can make use of the photoelectric effect equation:
E = hf = φ + qV
where:
E is the energy of a photon (given by hf, where h is the Planck constant and f is the frequency),
φ is the work function (minimum energy required to remove an electron from the metal),
q is the charge of an electron (1.6 x 10^-19 C), and
V is the stopping potential applied.
From the given data, we have:
For wavelength x = 3000 Å (Angstroms) and stopping potential V = 0.82 volts:
E = hf = φ + qV1
For wavelength x = 4000 Å and stopping potential V = 1.85 volts:
E = hf = φ + qV2
To determine (a) the value of the Planck constant, (b) the work function of sodium, and (c) the threshold wavelength of sodium, we can follow these steps:
(a) Determine the value of the Planck constant:
The energy of a photon can be calculated using the values of frequency (f) and wavelength (λ) using the formula: E = hf = hc/λ, where c is the speed of light.
First, convert the given wavelength values to meters:
λ1 = 3000 Å = 3000 x 10^-10 m
λ2 = 4000 Å = 4000 x 10^-10 m
Now, rearrange the equation E = hf to calculate the Planck constant (h):
h = E/f = (φ + qV) / f
We need to find the difference in energy (E) between the two wavelengths, which can be calculated as follows:
ΔE = E2 - E1 = (φ + qV2)/f2 - (φ + qV1)/f1
Substituting in the values we have:
ΔE = (φ + qV2) / cλ2 - (φ + qV1) / cλ1
By rearranging the equation, we can solve for the Planck constant (h):
h = ΔE * c * (1 / (λ2 - λ1))
Substitute the values of ΔE, c, and λ2 - λ1 into the equation to obtain the value of the Planck constant.
(b) Determine the work function of sodium in electron volts:
From the equation E = φ + qV, we can rearrange it to solve for the work function φ:
φ = E - qV
Substituting the values of E and V for one of the wavelengths, we can calculate the work function φ.
(c) Determine the threshold wavelength of sodium:
The threshold wavelength (λ_threshold) is the wavelength at which the stopping potential V becomes zero. At this point, the energy of the photon is just equal to the work function:
E = φ + qV_threshold
Since V_threshold = 0, the equation becomes:
E = φ
Rearrange the equation to solve for the threshold wavelength (λ_threshold):
λ_threshold = hc / φ
Substitute the values of h and c already calculated, along with the value of the work function φ, to find the threshold wavelength.
By following these steps, you can determine the value of the Planck constant, the work function of sodium, and the threshold wavelength of sodium using the given data.