Problem solving tips

## Dual Nature Of Radiation And Matter

- Want to score better marks in exams? Have a look at some problem solving tips.
1
Tip-1: Calculating the kinetic energy of photoelectrons
When light of suitable energy is incident on a metal surface, photoelectrons are emitted from the surface. many times we are asked to calculate the maximum kinetic energy of the photoelectrons.
Maximum Kinetic energy of photoelectrons = Energy of the incident light - Work function
Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).
Electrons accelerated by potential V are diffracted from a crystal. If and , V should be about :

A
V
B
V
C
V
D
V
With the decrease in the wave length of the incident radiation the velocity of the photoelectrons emitted from a given metal
A
Remains same
B
Increases
C
Decreases
D
Increases first and then decreases
2
Tip-2: Converting energy into the unit of electron-volt
We usy denote energy in the unit of joule. But in case of photoelectric emission or X-ray production, it is convenient to use energy in terms of electron-volt. We get energy in electron volt by dividing the energy in joule by the charge of electron. .uall
The frequency of a photon associated with an energy of 3.31 eV is (given h Js)
A
B
C
D
3
Tip-3: Determining hard X-rays and soft X-rays
Hard X-rays have high energy. One can easily determine the energy of X-ray by measuring its wavelength and vice-versa. The maximum possible energy of X-ray = Kinetic energy of electrons moving in a potential. Finally, .
In an x-ray tube, x-rays are produced by electrons accelerated by V volt. The maximum frequency of x-rays produced is
A
eVh
B
C
D
An X-Ray tube operates at a p.d. of . The wavelength of the highest frequency X-Rays emitted by this tube is nearly:()
A
B
C
D
4
Tips-4 :Finding the graphical relationship between two parameters
The maximum kinetic energy () of emitted photoelectrons against frequency of incident radiation is plotted as shown in fig. The slope of the graph is equal to
A
Charge on electron
B
Work function of emitter
C
Plancks constant
D
Ratio of Plancks constant and charge on electron
The graph between the de Broglie wavelength and the momentum of a photon is a
A
Rectangular hyperbola
B
Circle
C
Parabola
D
Straight line
The given graph shows the variation of   vs for characteristics X-rays. Lines 1, 2, 3, 4 shown in the graph corresponds to any one of  then is represented by  frequency, Atomic number
A
Line 1
B
Line 2
C
Line 3
D
Line 4
A photoelectric cell is connected to a source of variable potential difference, connected across it and the photoelectric current resulting is plotted against the applied potential difference (V). The graph in the broken line represents one for a given frequency and intensity of the incident radiation. If the frequency is increased and the intensity is reduced, then which of the following graphs of unbroken line represents the new situation?
A
A
B
B
C
C
D
D
In a photoelectric emission, electrons are ejected from metals X and Y by light of frequency f. The potential difference V required to stop the electrons is measured for various frequencies. If y has a greater work function than X, which graph illustrates the expected results?
A
B
C
D