51. The wavelength of a 1 keV photon is 1.24 × 10^–9 m. What is the frequency of 1 MeV photon?

1. 1. 1.24 × 10¹⁵​

   
   
   

   2. 2.4 × 10²⁰

   
   
   

   3. 1.24 × 10¹⁸

   
   
   

   4. 2 × 4 × 10²³

   
   
   

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   Here,
   

   	hc	= 103 eV and hv = 106 eV
   	λ

   
   Hence,
   

   v =	103c	=	103 × 3 × 108
   	λ		1.24 × 10-19

   
   = 2.4 × 10²⁰ Hz

   Correct Option: B

   Here,
   

   	hc	= 103 eV and hv = 106 eV
   	λ

   
   Hence,
   

   v =	103c	=	103 × 3 × 108
   	λ		1.24 × 10-19

   
   = 2.4 × 10²⁰ Hz

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52. Photoelectric work function of a metal is 1eV. Light of wavelength λ = 3000 Å falls on it. The photo electrons come out with velocity

1. 1. 10 metres/sec ​

   
   
   

   2. 10² metres/sec ​

   
   
   

   3. 10⁴ metres/sec

   
   
   

   4. 10⁶ metres/sec

   
   
   

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   hv = W +	1	mv2
   	2

   
   

   or	hc	= W +	1
   	λ		mv2

   
   Here λ = 3000 Å = 3000 × 10^–10 m
   ​and W = 1 eV = 1.6 × 10^–19 joule
   

   ∴	(6.6 × 10-34)(3 × 108)
   	3000 × 10-10

   
   

   = (1.6 × 10-19) +	1	× (9.1 × 10-31)v2
   	2

   
   Solving we get,
   v ≌ 10⁶ m/s

   Correct Option: D

   hv = W +	1	mv2
   	2

   
   

   or	hc	= W +	1
   	λ		mv2

   
   Here λ = 3000 Å = 3000 × 10^–10 m
   ​and W = 1 eV = 1.6 × 10^–19 joule
   

   ∴	(6.6 × 10-34)(3 × 108)
   	3000 × 10-10

   
   

   = (1.6 × 10-19) +	1	× (9.1 × 10-31)v2
   	2

   
   Solving we get,
   v ≌ 10⁶ m/s

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53. Energy levels A, B, C of a certain atom correspond to increasing values of energy i.e., E_A < E_B < E_C. If λ₁, λ₂, λ₃ are the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A respectively, which of the following relation is correct?

1. 1. λ₃ = λ₁ + λ₂

   
   
   

   2. λ3 =	λ1λ2
      	λ1 + λ2

   
   
   

   3. λ₁ + λ₂ + λ₃ = 0

   
   
   

   4. λ₃² = λ₁² + λ₂²

   
   
   

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   (E2 - E1) = hv =	hc
   	λ

   
   

   ∴	hc	= (EC - EB),	hc	= (EB - EA)
   	λ1		λ2

   
   

   and	hc	= (EC - EA)
   	λ3

   
   Now,
   (E_C - E_A) = (E_C - E_B) + (E_B - E_A)
   

   or,	hc	=	hc	+	hc
   	λ3		λ1		λ2

   
   

   or	1	=	1	+	1
   	λ3		λ1		λ2

   
   

   ∴	1	=	λ1 + λ2
   	λ3		λ1λ2

   
   

   or λ3 =	λ1λ2
   	λ1 + λ2

   Correct Option: B

   (E2 - E1) = hv =	hc
   	λ

   
   

   ∴	hc	= (EC - EB),	hc	= (EB - EA)
   	λ1		λ2

   
   

   and	hc	= (EC - EA)
   	λ3

   
   Now,
   (E_C - E_A) = (E_C - E_B) + (E_B - E_A)
   

   or,	hc	=	hc	+	hc
   	λ3		λ1		λ2

   
   

   or	1	=	1	+	1
   	λ3		λ1		λ2

   
   

   ∴	1	=	λ1 + λ2
   	λ3		λ1λ2

   
   

   or λ3 =	λ1λ2
   	λ1 + λ2

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54. A radio transmitter operates at a frequency 880 kHz and a power of 10 kW. The number of photons emitted per second is

1. 1. 1.72 × 10³¹

   
   
   

   2. 1.327 × 10²⁵

   
   
   

   3. 1.327 × 10³⁷

   
   
   

   4. ​1.327 × 10⁴⁵

   
   
   

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   No. of photons emitted per sec,
   

   n =	Power
   	Energy of photon

   
   

   =	P	=	10000
   	hv		6.6 × 10-34 × 880 × 103

   
   = 1.72 × 10³¹

   Correct Option: A

   No. of photons emitted per sec,
   

   n =	Power
   	Energy of photon

   
   

   =	P	=	10000
   	hv		6.6 × 10-34 × 880 × 103

   
   = 1.72 × 10³¹

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55. The momentum of a photon of an electromagnetic radiation is 3.3 × 10^–29​ kg ms^–1. What is the frequency of the associated waves ?
    ​[h = 6.6 × 10^–34 Js; c = 3 × 10⁸ ms^–1)

1. 1. 1.5 × 10¹³ Hz ​

   
   
   

   2. 7.5 × 10¹² Hz

   
   
   

   3. 6.0 × 10³ Hz ​

   
   
   

   4. 3.0 × 10³ Hz

   
   
   

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   As λ =	h	and λ =	c	;
   	P		v

   
   

   so v =	c	=	cP
   	λ		h

   
   

   3 × 108 × =	3.3 × 10-29
   	6.6 × 10-34

   
   = 1.5 × 10¹³ Hz

   Correct Option: A

   As λ =	h	and λ =	c	;
   	P		v

   
   

   so v =	c	=	cP
   	λ		h

   
   

   3 × 108 × =	3.3 × 10-29
   	6.6 × 10-34

   
   = 1.5 × 10¹³ Hz

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