11. In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is

1. 1. 	9
      	4

   
   
   

   2. 	27
      	5

   
   
   

   3. ​

      	5
      	27

   
   
   

   4. 	4
      	9

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​For Lyman series (2 → 1)
   

   	1	= R		1 -	1		=	3R
   	λL				22			4

   
   For Balmer series  (3 → 2)
   

   1	= R		1	-	1		=	5R
   λB			4		9			36

   
   
   

   ⇒		=	4
   	λL		3R
   	λB		36
   			5R

   Correct Option: D

   ​For Lyman series (2 → 1)
   

   	1	= R		1 -	1		=	3R
   	λL				22			4

   
   For Balmer series  (3 → 2)
   

   1	= R		1	-	1		=	5R
   λB			4		9			36

   
   
   

   ⇒		=	4
   	λL		3R
   	λB		36
   			5R

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12. In a Rutherford scattering experiment when a projectile of charge Z₁ and mass M₁approaches a target nucleus of charge Z₂ and mass M₂, the distance of closest approach is r₀. The energy of the projectile is​​

1. 1. directly proportional to Z₁ Z₂

   
   
   

   2. inversely proportional to Z₁

   
   
   

   3. directly proportional to mass M₁

   
   
   

   4. directly proportional to M₁ ×  M₂

   
   
   

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1. View Hint View Answer Discuss in Forum

   The kinetic energy of the projectile is given by
   

   	1	mv2 =	Ze(2e)	=	Z1 Z2
   	2		4πε0r0		4πε0r0

   
   Thus energy of the projectile is directly proportional to Z₁, Z₂

   Correct Option: A

   The kinetic energy of the projectile is given by
   

   	1	mv2 =	Ze(2e)	=	Z1 Z2
   	2		4πε0r0		4πε0r0

   
   Thus energy of the projectile is directly proportional to Z₁, Z₂

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13. Who indirectly determined the mass of the electron by measuring the charge of the electron?

1. 1. Millikan

   
   
   

   2. Rutherford

   
   
   

   3. Einstein

   
   
   

   4. Thomson

   
   
   

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1. View Hint View Answer Discuss in Forum

   Thomson

   Correct Option: D

   Thomson

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14. J.J. Thomson’s experiment demonstrated that

1. 1. the e/m ratio of the cathode-ray particles changes when a different gas is placed in the discharge tube ​

   
   
   

   2. cathode rays are streams of negatively charged ions ​

   
   
   

   3. all the mass of an atom is essentially in the nucleus ​

   
   
   

   4. the e/m of electrons is much greater than the e/m of protons

   
   
   

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1. View Hint View Answer Discuss in Forum

   Cathode rays are streams of negatively charged ions

   Correct Option: B

   Cathode rays are streams of negatively charged ions

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15. ​In Rutherford scattering experiment, what will be the correct angle for α-scattering for an impact parameter, b = 0 ?

1. 1. 90°

   
   
   

   2. 270°

   
   
   

   3. 0°

   
   
   

   4. 180°

   
   
   

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1. View Hint View Answer Discuss in Forum

   Impact parameter for Rutherford scattering experiment,
   

   b =	Ze2 cot(θ/2)	= 0 ⇒ cot(θ/2) = 0
   	4π∊0ki

   
   

   ⇒	θ	= 90° or θ = 180°
   	2

   Correct Option: D

   Impact parameter for Rutherford scattering experiment,
   

   b =	Ze2 cot(θ/2)	= 0 ⇒ cot(θ/2) = 0
   	4π∊0ki

   
   

   ⇒	θ	= 90° or θ = 180°
   	2

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