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1

AIEEE 2005

MCQ (Single Correct Answer)
A photocell is illuminated by a small bright source placed $$1$$ $$m$$ away. When the same source of light is placed $${1 \over 2}$$ $$m$$ away, the number of electrons emitted by photo-cathode would
A
increases by a factor of $$4$$
B
decreases by a factor of $$4$$
C
increases by a factor of $$2$$
D
decreases by a factor of $$2$$

Explanation

$$I \propto {1 \over {{r^2}}};{{{I_1}} \over {{I_2}}} = {\left( {{{{r_2}} \over {{r_1}}}} \right)^2} = {1 \over 4}$$

$${I_2} \to 4\,\,$$ times $${I_1}$$

When intensity becomes 4 times, no. of photoelectrons emitted would increase by $$4$$ times, since number of electrons emitted per second is directly proportional to intensity.
2

AIEEE 2005

MCQ (Single Correct Answer)
If the kinetic energy of a free electron doubles, it's deBroglie wavelength changes by the factor
A
$$2$$
B
$${1 \over 2}$$
C
$${\sqrt 2 }$$
D
$${1 \over {\sqrt 2 }}$$

Explanation

de-Broglie wavelength,

$$\lambda = {h \over p} = {h \over {\sqrt {2.m,\left( {K.E} \right)} }}$$

$$\therefore$$ $$\lambda \propto {1 \over {\sqrt {K.E} }}$$

If $$K.E$$ is doubled, wavelength becomes $${\lambda \over {\sqrt 2 }}$$
3

AIEEE 2004

MCQ (Single Correct Answer)
According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal $$Vs$$ the frequency, of the incident radiation gives as straight the whose slope
A
depends both on the intensity of the radiation and the metal used
B
depends on the intensity of the radiation
C
depends on the nature of the metal used
D
is the same for the all metals and independent of the intensity of the radiation

Explanation

From Equation $$K.E = hv - \phi $$

slope of graph of $$K.E$$ and $$v$$ is = $$h$$ (Plank's constant) which is same for all metals.
4

AIEEE 2004

MCQ (Single Correct Answer)
The work function of a substance is $$4.0$$ $$eV.$$ The longest wavelength of light that can cause photo-electron emission from this substance is approximately.
A
$$310$$ $$nm$$
B
$$400$$ $$nm$$
C
$$540$$ $$nm$$
D
$$220$$ $$nm$$

Explanation

For the longest wavelength to emit photo electron

$${{hc} \over \lambda } = \phi \Rightarrow \lambda = {{hc} \over \phi }$$

$$ \Rightarrow \lambda = {{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}} \over {40 \times 1.6 \times {{10}^{ - 16}}}} = 310nm$$

Questions Asked from Dual Nature of Radiation

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