Rutherford's Set up and Predictions

Q.

Activities of three radioactive substances $A$, $B$ and $C$ are represented by the curves $A$, $B$ and $C$ , in the figure. Then their half-lives $T_{1/2}\left(A\right):T_{1/2}\left(B\right):T_{1/2}\left(C\right)$ are in the ratio:

1. $3:2:1$

2. $2:1:1$

3. $4:3:1$

4. $2:1:3$

Q. Two circular loops of radii $0.05\text{m}$ and $0.09\text{m}$ are arranged such that their axes coincide and their centres are $0.12\text{m}$ apart. Charge of ${10}^{-6}\text{C}$ is spread uniformly on each loop. The potential difference between the centres of the loops is

1. $64\text{kV}$
2. $71\text{kV}$
3. $82\text{kV}$
4. $95\text{kV}$

Q.

Maximum kinetic energy of the positive ion in the cyclotron is

Q. The variation of electric potential $\left(V\right)$ with distance $\left(r\right)$ from a fixed point is as shown in the figure. Electric field intensity $(\text{in V/m)}$ at $r=1\text{m},3\text{m}$ and $4.5\text{m}$ are respectively

1. $-2,1,\frac{8}{3}$
2. $-2,0,\frac{8}{3}$
3. $2,0,-\frac{8}{3}$
4. $+8,-1,-\frac{4}{3}$

Q.

What is the Importance of Compton Effect.

Q. Find the mass defect of the $\text{Helium}-4$ nucleus.

Given mass of the helium nucleus $M_{\text{He}}=4.0015084u$
Mass of a proton $m_p=1.007276u$
Mass of a neutron $m_n=1.008665u$

1. $0.30374u$
2. $0.030374u$
3. $0.030384u$
4. $0.03074u$

Q.

In an experiment, the initial number of radioactive nuclei is $3000$. It is found that $1000\pm 40$ nuclei decayed in the first $1.0\sec$. For $\left|\mathrm{x}\right|<<1$, $\mathrm{In}(1+\mathrm{x})=\mathrm{x}$ up to the first power in $\mathrm{x}$. The error $\mathrm{\Delta \lambda }$, in the determination of the decay constant $\mathrm{\lambda }$, in ${\mathrm{s}}^{-1}$ is

1. $0.04$

2. $0.03$

3. $0.02$

4. $0.01$

Q. the photon and electron both have wavelength 1 angstorm the ratio of their energy?

Q. What percentage of the atoms in a sample will remain undecayed in a time equal to mean life?

1. 100%
2. 63%
3. 50 %
4. 37 %

Q. Two radioactive samples of different elements having half lives $t_1$ and $t_2$ respectively, have the same number of nuclei at $t=0$. The time after which their activities are the same is

1. $\frac{t_1{t}_2}{0.693}\ln \left(\frac{t_2}{t_1}\right)$
2. $\frac{t_1{t}_2}{0.693(t_2-t_1)}\ln \left(\frac{t_2}{t_1}\right)$
3. $\frac{t_1{t}_2}{0.693(t_2+t_1)}\ln \left(\frac{t_2}{t_1}\right)$
4. $\frac{0.693}{t_1{t}_2}\ln \left(\frac{t_2}{t_1}\right)$

Q. ntThe de Broglie the de Broglie wavelength of an electron moving with velocity C/2(C= velocity of light in vaccum) is equal to the wavelength of a Photon. The ratio of kinetic energies of electron and Photon is:n nta. 1:4 b. 1:2 c. 4:1 d. 2:1n

Q. If a radioactive sample emits n beta particles in t second and emits 0.75n beta particles in next t second. Find mea life of sample.

Q. Two charges $12\mu \text{C}$ and $-6\mu \text{C}$ are separated by a distance of $20\text{cm}$. The net electric potential is zero at a point between the charges and on the line joining them will be

1. At a distance of $6.7\text{cm}$ from $12\mu \text{C}$
2. At a distance of $13.3\text{cm}$ from $12\mu \text{C}$
3. At a distance of $16.7\text{cm}$ from $-6\mu \text{C}$
4. At a distance of $8.7\text{cm}$ from $-6\mu \text{C}$

Q. Kinetic mass of photon?

Q. In scattering experiment find the distance of closest approach if a 6MeV alpha -particle is used (1) 3.2times10^(-16)m (2) 3.79times10^(-14)m (3) 4.6times10^(-15)m (4) 3.2times10^(-15)m

Q. 42.The counting rate observed from a Radioactive source of t=0 second was 1600 count as per second and t=8 seconds it was 100 counters per second the counting rate observed as counters per second is equal to 6 seconds will be

Q. the wavelength of electron and wavelength of photon of same energy E are related as

Q. Assume that an electric field $\overrightarrow{E}=30x^2\hat{i}$ exists in space. Then the potential difference $V_A-V_0$, where $V_0$ is the potential at the origin and $V_A$ the potential at $x=2\text{m}$, is :

1. $-120\text{J}$
2. $80\text{J}$
3. $120\text{J}$
4. $-80\text{J}$

Q. A photon and an electron both have wavelength 1A the ratio of energy of photon to that of electron is a) 1 b)0.012 c)82.7

Q. An arc of radius $r$ carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle of $\pi /3$ at the centre. What is electric potential at the centre?

1. $\frac{\lambda }{16{ϵ}_o}$
2. $\frac{\lambda }{4{ϵ}_o}$
3. $\frac{\lambda }{8{ϵ}_o}$
4. $\frac{\lambda }{12{ϵ}_o}$

Q. The variation of electric potential $\left(V\right)$ with distance $\left(r\right)$ from a fixed point is as shown in the figure. Electric field intensity $(\text{in V/m)}$ at $r=1\text{m},3\text{m}$ and $4.5\text{m}$ are respectively

1. $+8,-1,-\frac{4}{3}$
2. $2,0,-\frac{8}{3}$
3. $-2,1,\frac{8}{3}$
4. $-2,0,\frac{8}{3}$

Q. ntthe ratio of number of collisions per sec at the wall of the contaners by he and O2 gas molecules kept at same volume and temperature , is( assume normal incidence on walls) n

Q. A proton and an $\alpha -$ particle, having kinetic energies $K_p$ and $K_{\alpha }$ respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $\alpha -$ particle is $2:1$. The ratio $K_p:K_{\alpha }$ will be :

1. $1:8$
2. $1:4$
3. $8:1$
4. $4:1$

Q. I. The atom is mostly empty space.
II. Electrons orbit the nucleus of the atom.
III. The atom has a dense, positively charged nucleus.

1. I only
2. II only
3. I, II, and III
4. II and III only
5. I and II only

Q. Which ray/radiation can be detected by GM counter?

1. Alpha
2. Beta
3. $\gamma$ ray
4. all

Q. What conclusion was drawn by Rutherford based on Geiger-Marsden's experiment on scattering of alpha particles?

Q. an electron in hydrogen atom makes a transition from n=5 to n=1. find max. no of photons emitted

Q.

Are the nucleons fundamental particles, or do they consist of still smaller parts? One way to find out is to probe a nucleon just as Rutherford probed an atom. What should be the kinetic energy of an electron for it to be able to probe a nucleon? Assume the diameter of a nucleon to be approximately ${10}^{–15}$ m.

Q. A high energy photon collides elastically with a charged particle (usually an electron)., The photon "bounces away" with less energy (a longer wavelength).
The process described here is known as :

1. Compton scattering
2. The photoelectric effect
3. X-ray production
4. Annihilation
5. Quantum tunneling

Q.

Assertion (A): The source of $\alpha$- particles are taken in a lead block.

Reason (R): Some radioactive emanations can penetrate through lead block.

1. Both A and R are true and R is the correct explanation of A.

2. Both A and R are true, but R is not the correct explanation of A.

3. A is true and R is false.

4. A is false and R is true.