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The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is
1. $\frac{1}{2}$
2. $\frac{2}{237}$
3. $\frac{1}{237}$
4. $\frac{1}{137}$

The first member of Balmer series of H-atom has a wavelength 6561Å . The wavelength of second member will be
1. 6860 Å 
2. 5860 Å 
3. 4860 Å 
4. 3860 Å

In which of the following transitions will the wavelength be minimum in the case of hydrogen atom?
1. n = 5 to n = 4 
2. n = 4 to n = 3 
3. n = 3 to n = 2 
4. n = 2 to n = 1

Given that mass of proton = 1.00813 amu, mass of neutron is 1.00894 amu and mass of $\mathrm{\alpha }$-particle is 4.00388 amu, the binding energy of alpha particle is
1. 28.172 MeV 
2. 27.172 MeV 
3. 13.52 MeV 
4. 56.321 MeV

Nuclear radius of ${}_8{\mathrm{O}}^{16}$ is 3 fermi. The nuclear radius of ${}_{82}P{b}^{205}$ is
1. 5.02 fermi 
2. 6.02 fermi 
3. 7.02 fermi 
4. 8.02 fermi

What percentage of a radioactive substance is left after 5 half-lives
1. 31% 
2. 3.12% 
3. 0.3% 
4. 1%

At any instant the ratio of the amount of radioactive substances is 2 : 1. If their half-lives be respectively 12 and 16 hours, then after two days, what will be the ratio of the substances?
1. 1 : 1 
2. 2 : 1 
3. 1 : 2 
4. 1 : 4

The nucleus \(\mathrm C_{6}^{12 }\) absorbs an energetic neutron and emits particle \(\beta^-.\) The resulting nucleus is:
1. \(\mathrm N_{7}^{14 }\)                    
2. \(\mathrm N_{7}^{13 }\)                 
3. \(\mathrm B_{5}^{13 }\)                   
4. \(\mathrm C_{6}^{13 }\)

In the reaction represented by  _ZX^A $\to$ _{Z – 2}Y^{A – 4} $\to$ _{Z – 2}Y^{A – 4} $\to$ _{Z – 1}K^{A –4} . The decays in the sequence are                                               
1. $\mathrm{\alpha },\mathrm{\beta },\mathrm{\gamma }$
2. $\mathrm{\beta },\mathrm{\alpha },\mathrm{\gamma }$
3. $\mathrm{\gamma },\mathrm{\alpha },\mathrm{\beta }$
4. $\mathrm{\alpha },\mathrm{\gamma },\mathrm{\beta }$

The de Broglie wavelength of an electron in the n^th Bohr orbit is related to the radius R of the orbit as       
1. $\mathrm{n\lambda }=\mathrm{\pi R}$
2. $\mathrm{n\lambda }=\frac{3}{2}\mathrm{\pi R}$
3. $\mathrm{n\lambda }=2\mathrm{\pi R}$
4. $\mathrm{n\lambda }=4\mathrm{\pi R}$
 

Three radioactive substances have their activity in the ratio 1 : 3 : 5. The substances are heated to double its temperature. Then, the activity will be
1. 5 : 3 : 1
2. 3 : 1 : 5 
3. 3 : 5 : 1 
4. 1 : 3 : 5

In Bohr’s model, the atomic radius of the first orbit is r₀ ; then the radius of the third orbit is   
1. r₀/9                         
2. r₀                           
3. 9r₀                         
4. 3r₀

The diagram shows the energy levels for an electron in certain hydrogen like atom. Which transition shown represents the emission of a photon with the most energy?

1. (i) 
2. (ii)
3. (iii) 
4. (iv)

If the shortest wavelength of Lyman series of H atom is x, then the wavelength of first member of Balmer series of H atom will be
1. 9x / 5 
2. 36x / 5
3. 5x / 9 
4. 5x / 36s

An excited hydrogen atom emits a photon of wavelength, while returning to the ground state. The quantum number n of the excited state is given by (R = Rydberg constant)
1. $\sqrt{\mathrm{\lambda R}/\left(\mathrm{\lambda R}-1\right)}$
2. $\sqrt{\mathrm{\lambda R}/\left(\mathrm{\lambda R}+1\right)}$
3. $\sqrt{\left(\mathrm{\lambda R}-1\right)/\mathrm{\lambda R}}$
4. $\frac{1}{\sqrt{\mathrm{\lambda R}/\left(\mathrm{\lambda R}-1\right)}}$

Two radioactive materials X₁ and X₂ have decay constants 10 $\mathrm{\lambda }$ and $\mathrm{\lambda }$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X­₁ to that of X₂ will be 1/e after a time   
1. $\frac{1}{10\mathrm{\lambda }}$
2. $\frac{1}{11\mathrm{\lambda }}$
3. $\frac{11}{10\mathrm{\lambda }}$
4. $\frac{1}{9\mathrm{\lambda }}$

A container is filled with a radioactive substance for which the half-life is 2 days. Six days later, when the container is opened, it contains 5 grams of the substance. How many grams of the substance were initially placed in the container?
1. 40 
2. 60 
3. 80 
4. 100

The radioactivity of a sample is R₁ at a time T₁ and R₂ at a time T₂. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T₂ – T₁) is proportional to      
1. ${\mathrm{R}}_1{\mathrm{T}}_1-{\mathrm{R}}_2{\mathrm{T}}_2$
2. ${\mathrm{R}}_1-{\mathrm{R}}_2$
3. $\frac{{\mathrm{R}}_1-{\mathrm{R}}_2}{\mathrm{T}}$
4. $\left({\mathrm{R}}_1-{\mathrm{R}}_2\right)T$

The activity of a radioactive element decreases to one-third of the original activity I₀ in a period of nine years. After a further lapse of nine years its activity will be    
1. I₀                           
2.(2/3) I₀                     
3. (I₀/9)                       
4. (I₀/6)
 

An unknown atom has 30 neutrons in its nucleus. Ratio of radii of nuclei of this  atom and ${}_2{}^4\mathrm{He}$ is ${\left(14\right)}^{1/3}$. Then the atomic number of unknown atom is
1. 28                           
2. 26                           
3. 30                           
4. 31