**Photoelectric effect**: If an

__EM wave with sufficiently high frequency__is shone on a piece of metal,

__electrons will be emitted__from the metal surface.

Experiment on photoelectric effect:

Put a UV lamp against the zinc plate on a gold leaf electroscope.

1) When zinc plate is

__negatively charged__, gold leaf fall as UV radiation strikes on it because**electrons (negative charge) are emitted away**.2) The gold leaf

__stopped falling if barrier exist__between the lamp and the zinc plate.3) When zinc plate is

__positively charged__, gold leaf will not fall because__electrons can’t escape due to electrostatic attraction__between zinc plate (+) and electron (-).**Photocell**is composed by a metal plate (cathode) and an electrode (anode). Under exposure of EM wave with sufficiently high frequency, it emits electron. When it’s connected with voltage supply and ammeter, photoelectric current can be measured.

1) Consider anode with a higher potential, the photoelectric effect occurs normally.

2) When anode has a lower potential,

__the current direction is still the same__but the photoelectric current is decreasing.**3)**

**At a certain potential (-V**

_{s}) the photoelectric current becomes zero. We say that V_{s}is the stopping potential of the cell.4) At stopping potential even electrons with highest K.E. can’t reach the anode. Therefore

**K.E.**_{max}= eV_{s}5) A smaller unit of energy, electron-volt,

**1eV = (e)(V) = 1.6*10**. This is equal to the^{-19}J__gain of energy when electron accelerates through a p.d. of 1V__.**Properties of photoelectric effect**

1)

__Electrons emitted only when f ≥ f__, the threshold frequency._{0}2)

__Number of photoelectrons (per second) is proportional to radiation intensity__.3)

__K.E.__._{max}increases with frequency4)

__Photoelectric effect is immediate__, i.e., once radiation with sufficiently high frequency is given to the metal plate, electrons are emitted at once.Explaining photoelectric effect by

**classical wave theory**:- Wave energy transmitted in a

**continuous manner**and spreads over the wavefront.-

**Energy transfer rate is independent of frequency**.The wave theory cannot explain property 1,3 and 4. Here’s the

**contradictory result by wave theory**on the properties of photoelectric effect:Property 1: Energy is independent of frequency so it should happen for all frequency.

Property 3: Energy is independent of frequency so as K.E.

_{max}.Property 4: Since energy transfer is continuous, there’s delay before electrons get enough energy to escape.

**Quantum theory**: quantizing light wave into

__discrete packets__, called

__light quanta__or

__photons__.

The energy of each photon is related to its frequency,

**E=hf**, where h is the**Planck constant**, which is**6.63 * 10**.^{-34}J sNote that the behavior of photon is discrete instead of continuous manner.

Since K.E. of photoelectron = energy absorbed – energy used to escape the metal, we have

**Einstein’s photoelectric equation: K.E.**, where Φ is the_{max}= hf – Φ**work function**, in terms of eV, subjective to the metal used. (usually inversely related to its reactivity.)The quantum theory can explain most of the photoelectric effect:

Property 1: threshold frequency is given by

__hf__. Therefore we also have_{0}= Φ__K.E.__._{max}= h(f – f_{0})Property 2: Intensity is proportional to rate of photons transmitted, so it’s also proportional to the photoelectrons emitted.

Property 3: true by K.E.

_{max}= hf – Φ.Property 4: true since electron gain enough energy once it absorb the photon.

**Experimental verification**of K.E.

_{max}= hf – Φ by showing

**V**

_{s}= (h/e) f –Φ/eDirect a beam of monochromatic light of frequency f, the photoelectrons complete the circuit with voltage supply and galvanometer. V

_{s}is found when the readings of galvanometer drops to zero. A V_{s}-f graph has x,y-intercept f_{0}and –Φ/e respectively, and slope h/e. Note that the slope is a constant and applicable to all metal and frequency.By the above equation we have:

- V

_{s}is independent of intensity, but intensity is proportional to photoelectric current (I_{p}).- Under the same intensity, light with higher frequency has larger V

_{s}but lower I_{p}.
## No comments:

## Post a comment