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1

JEE Main 2019 (Online) 12th January Morning Slot

MCQ (Single Correct Answer)
A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $${{{\lambda _A}} \over {{\lambda _B}}}$$ is close to :
A
4.47
B
10.00
C
14.14
D
0.07

Explanation

K.E. acquired by charge = K = qV

$$\lambda $$ = $${h \over P}$$ = $${h \over {\sqrt {2mK} }}$$ = $${h \over {\sqrt {2mqV} }}$$

$$ \therefore $$  $${{{\lambda _A}} \over {{\lambda _B}}} = {{\sqrt {2m{}_B{q_B}{V_B}} } \over {\sqrt {2m{}_A{q_A}{V_A}} }} = \sqrt {{{4m.q.2500} \over {m.q.50}}} = 2\sqrt {50} $$

$$ = 2 \times 7.07 = 14.14$$
2

JEE Main 2019 (Online) 11th January Evening Slot

MCQ (Single Correct Answer)
In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to: ($${{{hc} \over e}}$$ = 1240 nm$$-$$V)
A
0.5 V
B
1.0 V
C
2.0 V
D
1.5 V

Explanation

$${{hc} \over {{\lambda _1}}} = \phi + e$$V1        . . . (i)

$${{hc} \over {{\lambda _2}}} = \phi + e$$V2        . . . (ii)

(i) $$-$$ (ii)

hc$$\left( {{1 \over {{\lambda _1}}} - {1 \over {{\lambda _2}}}} \right)$$ = e(V1 $$-$$ V2)

$$ \Rightarrow $$  V1 $$-$$ V2 = $${{hc} \over e}$$$$\left( {{{{\lambda _2} - {\lambda _1}} \over {{\lambda _1} - {\lambda _2}}}} \right)$$

= (1240nm $$-$$ V) $${{100nm} \over {300nm \times 400nm}}$$

= 1V
3

JEE Main 2019 (Online) 11th January Morning Slot

MCQ (Single Correct Answer)
If the de Broglie wavelength of an electron is equal to the 10–3 times the wavelength of a photon of frequency 6 $$ \times $$ 1014 Hz, then the speed of electron is equal to : (Speed of light = 3 $$ \times $$ 108 m/s, Planck's constant = 6.63 $$ \times $$ 10–34 J.s, Mass of electron = 9.1 $$ \times $$ 10–31 kg)
A
1.7 $$ \times $$ 106 m/s
B
1.45 $$ \times $$ 106 m/s
C
1.1 $$ \times $$ 106 m/s
D
1.8 $$ \times $$ 106 m/s

Explanation

$${h \over {mv}} = {10^{ - 3}}\left( {{{3 \times {{10}^8}} \over {6 \times {{10}^{14}}}}} \right)$$

v $$ = {{6.63 \times {{10}^{ - 34}} \times 6 \times {{10}^{14}}} \over {9.1 \times {{10}^{ - 31}} \times 3 \times {{10}^5}}}$$

v $$ = 1.45 \times {10^6}$$ m/s
4

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)
A metal plate of area 1 $$ \times $$ 10–4 m2 is illuminated by a radiation of intensity 16 mW/m2. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. The number of emitted photoelectrons per second and their maximum energy, respectively, will be
A
1014 and 10 eV
B
1012 and 5 eV
C
1011 and 5 eV
D
1010 and 5 eV

Explanation

Given, $$\phi $$ = 5 eV, E = 10 eV

$$ \therefore $$ KE = E – $$\phi $$ = 10 – 5 = 5 eV

Energy incident on the plate,

E' = $$\left( {16 \times {{10}^{ - 3}}} \right)\left( {1 \times {{10}^{ - 4}}} \right)$$

= 16 $$ \times $$ 10-7 J/s

= 1013 eV/s

Number of photons emitted per second

= 10% of $${{E'} \over E} = 0.1 \times {{{{10}^{13}}} \over {10}}$$ = 1011 s-1

Questions Asked from Dual Nature of Radiation

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