In a photoelectric effect experiment, the stopping potential is measured for monochromatic light beams of varying wavelengths. The collected data is as follows:
wavelength (nm) $350$ $400$ $450$ $500$ $550$
stopping potential (V) $1.45$ $1.00$ $0.66$ $0.38$ $0.16$

Determine the Planck constant from this data.

Question

In a photoelectric effect experiment, the stopping potential is measured for monochromatic light beams of varying wavelengths. The collected data is as follows:

wavelength (nm)	$350$	$400$	$450$	$500$	$550$
stopping potential (V)	$1.45$	$1.00$	$0.66$	$0.38$	$0.16$

Determine the Planck constant from this data.

Quantrex Academy · Accepted Answer

Correct answer: C. 4.2 × 10^ -15 eV s

Einstein's photoelectric equation is given by:

eV_s = \dfrac{hc}{\lambda} - \Phi

V_s = \dfrac{hc}{e} \left(\dfrac{1}{\lambda}\right) - \dfrac{\Phi}{e}

The slope of the

V_s

versus

\dfrac{1}{\lambda}

graph is

m = \dfrac{hc}{e}

.

Taking the data points

\lambda_1 = 350 \text{ nm}, V_{s1} = 1.45 \text{ V}

and

\lambda_2 = 400 \text{ nm}, V_{s2} = 1.00 \text{ V}

:

m = \dfrac{\Delta V_s}{\Delta \left(\dfrac{1}{\lambda}\right)} = \dfrac{1.45 - 1.00}{\dfrac{1}{350} - \dfrac{1}{400}} \text{ V nm}

m = \dfrac{0.45}{\dfrac{50}{140000}} = 0.45 \times 2800 = 1260 \text{ V nm}

Equating this to

\dfrac{hc}{e}

:

\dfrac{hc}{e} = 1260 \times 10^{-9} \text{ V m}

h = \dfrac{1260 \times 10^{-9} \text{ eV m}}{c} = \dfrac{1260 \times 10^{-9}}{3 \times 10^8} \text{ eV s}

h = 420 \times 10^{-17} \text{ eV s} = 4.2 \times 10^{-15} \text{ eV s}

In a photoelectric effect experiment, the stopping potential is...

Options

Correct answer

Step-by-step solution

More from Photoelectric Effect and Wave–Particle Duality