Friday, March 10, 2023

H C Verma solutions, BOHR'S MODEL AND PHYSICS OF THE ATOM, Chapter-43, OBJECTIVE-II, Concepts of Physics, Part-II

Bohr's Model and Physics of the Atom


OBJECTIVE-II


     1.  In a laboratory experiment on emission from atomic hydrogen in a discharge tube, only a small number of lines are observed whereas a large number of lines are present in the hydrogen spectrum of a star. This is because in a laboratory 

(a) the amount of hydrogen taken is much smaller than that present in the star

(b) the temperature of hydrogen is much smaller than that of the star 

(c) the pressure of hydrogen is much smaller than that of the star

(d) the gravitational pull is much smaller than that of the star.      


ANSWER: (b).   


EXPLANATION: The temperature of a star is much higher than that of the laboratory experiment. Hence the electrons get much higher energies to jump to the orbits of much higher energy levels. So when they jump down to lower orbits, they have many energy levels available. Thus radiations have a large range of wavelengths, so a large number of lines are present in the hydrogen spectrum. Option (b) is correct.  




      2.  An electron with kinetic energy 5 eV is incident on a hydrogen atom in its ground state. The collision 

(a) must be elastic

(b) may be partially elastic

(c) must be completely inelastic

(d) maybe completely inelastic.   


ANSWER: (a).   


EXPLANATION: The energy of a hydrogen atom in its ground state is -13.6 eV. The first excited state has an energy of -3.4 eV. So if the collision is inelastic, it needs to absorb at least energy equal to -3.4 -(-13.6) =10.2 eV. Thus in this case the colliding electron must have energy equal to 10.2 eV for completely inelastic collision or more than 10.2 eV for partially inelastic collision. In this case, the incident electron's energy is only 5 eV which can not be absorbed by the atom. So the collision will be elastic.

Option (a) is correct. 


 



     3.  Which of the following products in a hydrogen atom are independent of the Principal quantum number n? The symbols have their usual meanings. 

(a) vn 

(b) Er

(c) En

(d) vr.   


ANSWER: (a), (b).   


EXPLANATION: The relations among E, n, r, and v for a hydrogen-like atom are as follows. 

E =-mZ²e⁴/(8εₒ²h²n²) ----- (i)

r =εₒh²n²/(πmZe²) --------- (ii)

v =Ze²/(2εₒhn) ------------- (iii) 

From (iii), vn =Ze²/(2εₒh). It is independent of n. Option (a) is correct. 

From (i) and (ii), 

Er =-Ze²/(8πεₒ). It is also independent of n. So Option (b) is also correct. 

From (i), En =-mZ²e⁴/(8εₒh²n). Clearly, this product depends on n. Option (c) is not correct. 

From (ii) and (iii),

vr =hn/(2πm). So this product also depends on n. Option (d) is not correct.

     



     4.  Let Aₙ be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln(Aₙ/A₁) against ln(n)

(a) will pass through the origin

(b) will be a straight line with slope 4

(c) will be a monotonically increasing nonlinear curve

(d) will be a circle.   


ANSWER: (a), (b).   


EXPLANATION: The area of the nth orbit is,

Aₙ =πrₙ², and the area of the first orbit 

A₁ =πr₁².

But rₙ=n²aₒ. 

So, r₁ =aₒ.

Thus, Aₙ/A₁ =n⁴

→ln (Aₙ/A₁) =ln(n⁴) =4 ln(n)

It is in the form of y =4x. So the graph of ln (Aₙ/A₁) vs ln (n) will be a straight line that will pass through the origin with slope 4.

Options (a) and (b) are only correct. 




     5.  The ionization energy of a hydrogen-like ion A is greater than that of another hydrogen-like ion B. Let r, u, E, and L represent the radius of the orbit, speed of the electron, energy of the atom, and orbital angular momentum of the electron respectively. In ground state 

(a) rA > rB 

(b) uA > uB

(c) EA > EB

(d) LA > LB.   


ANSWER: (b).   


EXPLANATION: The ionization energy of a hydrogen-like ion with atomic number Z is given as, 

V =(13.6 eV)*Z². 

Hence the atomic number of A is greater than B. The radius of the orbit is inversely proportional to Z, so rA < rB. 

Option (a) is incorrect. 

The speed of the electron is directly proportional to Z. Hence uA > uB. 

Option (b) is correct.  

The energy of the ion is

E =-mZ²e⁴/(8εₒ²h²n²) 

Due to the negative sign, the Energy of A is less than B.  

Option (c) is incorrect.  

The orbital angular momentum does not depend on Z, it will be the same for ions in the ground state. 

Option (d) is also incorrect. 



 

 


     6.  When a photon stimulates the emission of another photon, the two photons have 

(a) same energy

(b) same direction 

(c) same phase

(d) same wavelength.   


ANSWER: All.   


EXPLANATION: When an atom emits a photon due to its interaction with a photon incident on it, the process is called stimulated emission. The emitted photon has exactly the same energy (hence the same wavelength), phase, and direction as the incident photon. 

So, all the options are correct. 

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Links to the Chapters


CHAPTER- 43- Bohr's Model and Physics of Atom



CHAPTER- 34- Magnetic Field

CHAPTER- 29- Electric Field and Potential











CHAPTER- 28- Heat Transfer

OBJECTIVE -I







EXERCISES - Q51 to Q55


CHAPTER- 27-Specific Heat Capacities of Gases

CHAPTER- 26-Laws of Thermodynamics


CHAPTER- 25-CALORIMETRY

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE-II


EXERCISES - Q-11 to Q-18


CHAPTER- 24-Kinetic Theory of Gases







CHAPTER- 23 - Heat and Temperature






CHAPTER- 17 - Light Waves




CHAPTER- 14 - Fluid Mechanics




CHAPTER- 13 - Fluid Mechanics


CHAPTER- 12 - Simple Harmonic Motion









CHAPTER- 11 - Gravitation





CHAPTER- 10 - Rotational Mechanics






CHAPTER- 9 - Center of Mass, Linear Momentum, Collision


CHAPTER- 8 - Work and Energy

Click here for → Question for Short Answers

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → Exercises (1-10)

Click here for → Exercises (11-20)

Click here for → Exercises (21-30)

Click here for → Exercises (31-42)

Click here for → Exercise(43-54)

CHAPTER- 7 - Circular Motion

Click here for → Questions for Short Answer 

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → EXERCISES (11-20)

Click here for → EXERCISES (21-30)

CHAPTER- 6 - Friction

Click here for → Questions for Short Answer

Click here for → OBJECTIVE-I

Click here for → Friction - OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → Exercises (11-20)

Click here for → EXERCISES (21-31)

For more practice on problems on friction solve these- "New Questions on Friction".

---------------------------------------------------------------------------------

CHAPTER- 5 - Newton's Laws of Motion


Click here for → QUESTIONS FOR SHORT ANSWER

Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)

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CHAPTER- 4 - The Forces

The Forces-

"Questions for short Answers"    


Click here for "The Forces" - OBJECTIVE-I


Click here for "The Forces" - OBJECTIVE-II


Click here for "The Forces" - Exercises


--------------------------------------------------------------------------------------------------------------

CHAPTER- 3 - Kinematics - Rest and Motion

Click here for "Questions for short Answers"


Click here for "OBJECTIVE-I"


Click here for EXERCISES (Question number 1 to 10)


Click here for EXERCISES (Question number 11 to 20)


Click here for EXERCISES (Question number 21 to 30)


Click here for EXERCISES (Question number 31 to 40)


Click here for EXERCISES (Question number 41 to 52)


CHAPTER- 2 - "Physics and Mathematics"

Click here for "Questions for Short Answers"


Click here for "OBJECTIVE-II"

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