Problem 3

Light of frequency

f

illuminates a metal with work function

\phi

. Find the maximum photoelectron kinetic energy and stopping potential; use Planck constant

h

and electron charge magnitude

e

. Each photon carries energy

hf

; electrons are emitted only when the light exceeds the threshold frequency. (a) Find threshold frequency

f_0

. (b) For

f>f_0

, find maximum kinetic energy

K_{max}

. (c) Find stopping potential

V_s

and state the emission condition. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

\boxed{f_0=\frac{\phi}{h},\quad K_{\max}=hf-\phi,\quad V_s=\frac{hf-\phi}{e}}

problems.proof.analysis

The final expressions are collected in the order requested and must satisfy the equations used above. Checking dimensions, signs, and limiting conditions catches algebra errors or omitted constraints.