The photoelectric effect equation relates the energy of incident photons, the work function of the material, and the maximum kinetic energy of emitted photoelectrons:
E‌photon ‌=φ+KEmaxThe maximum kinetic energy (
KEmax ) of the emitted photoelectrons is related to their maximum velocity (
vmax ) by the formula:
KEmax=‌mvmax2The stopping potential
(Vs) is the potential difference required to stop the most energetic photoelectrons. The work done by the stopping potential must be equal to the maximum kinetic energy of the electrons:
KEmax=eVsWe are given:
Work function
(φ)=1.5eV (Note: This is not directly needed to find the stopping potential if
vmax is given, but it would be needed to find the photon energy.)
Maximum velocity
(vmax)=8×105ms−1Mass of electron
(m)=9×10−31kgCharge of electron
(e)=1.6×10−19CFirst, calculate the maximum kinetic energy (
KE‌max ‌ ) using the given maximum velocity:
‌KEmax=‌mvmax2‌KEmax=‌×(9×10−31kg)×(8×105ms−1)2‌KEmax=‌×9×10−31×(64×1010) ‌KEmax=‌×9×64×10−31+10‌KEmax=9×32×10−21‌KEmax=288×10−21JNow, use the relationship between maximum kinetic energy and stopping potential (
KEmax=eVs ) to find the stopping potential (
Vs ):
‌Vs=‌‌Vs=‌| 288×10−21J |
| 1.6×10−19C |
‌Vs=‌×‌‌Vs=‌×10−2‌Vs=180×10−2‌Vs=1.8VThe stopping potential of the photoelectrons is 1.8 V .
The final answer is 1.8 V .
