Chemistry · Structure Of Atom · NEET
It is KE = hv - hv0, where h is Planck's constant (6.626 x 10^-34 J s), v is the frequency of the incoming light, and v0 is the threshold frequency of the metal. hv is the energy the photon carries in. hv0 (called the work function W0) is the minimum energy needed to pull an electron out. The difference is left over as the electron's kinetic energy. In short: KE = (photon energy) - (work function).
hv is the energy of the incoming photon, which depends on the light you shine. hv0 is a fixed property of the metal called the work function (W0) — it is the smallest energy needed to just free an electron. hv can change if you change the light's frequency, but hv0 never changes for a given metal. Electrons come out only when hv is bigger than hv0.
Because of energy conservation. The photon gives all its energy hv to one electron. The electron must first 'spend' energy W0 (= hv0) just to break free from the metal surface. Whatever energy is left after paying this cost becomes movement energy (kinetic energy). So KE = hv - W0. Nothing is created or lost — the photon's energy simply splits into 'escape cost' plus 'leftover speed'.
v0 is the minimum frequency of light that can eject an electron from that metal. If the light frequency v is less than v0, then hv is smaller than hv0, so KE would be negative — which is impossible. So NO electron comes out, no matter how bright the light is. NCERT gives the example: red light on potassium ejects nothing, but weak yellow light does, because potassium's v0 is 5.0 x 10^14 Hz.
No. Brightness (intensity) means MORE photons, so MORE electrons come out — but each electron still gets the same energy from one photon. Kinetic energy depends only on the frequency v, not on how bright the light is. To make electrons faster, you must increase the frequency, not the intensity. This is a very common NEET trap.
Find photon energy E = hv, or use E(eV) = 1240 / wavelength(nm) as a shortcut. Then KE = E - W0. Example (NCERT): photon of 4 x 10^-7 m has energy about 3.1 eV; if work function is 2.13 eV, then KE = 3.1 - 2.13 = about 0.97 eV. Convert to joules using 1 eV = 1.602 x 10^-19 J when you need velocity from KE = (1/2)mv^2.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
KE = hv - hv0, or equivalently KE = hv - W0, where W0 = hv0 is the work function. It can also be written as (1/2)mv^2 = hv - W0.
The work function W0 is the minimum energy needed to just eject an electron from the metal surface. It equals hv0, where v0 is the threshold frequency. It is a fixed property of each metal.
No. Kinetic energy depends only on the frequency of light. Intensity changes only the number of ejected electrons, not their speed.
No electrons are ejected at all, even if the light is very bright, because the photon energy hv is less than the work function hv0.
The maximum kinetic energy equals eV0, where V0 is the stopping potential. So eV0 = hv - W0, which links this equation to the stopping-potential experiment.
