## Numerical

In a radioactive decay process, the activity is defined as $A=-\frac{d N}{d t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two rad...

A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in these atoms are used to p...

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${ }_{7}^{16} \mathrm{~N}+$ ${ }_{2}^{4} \mathrm{He} \rightarrow{...

In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals P, Q and R are EP, EQ and ER, respectively, and they are rel...

A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency $$\Omega $$ such that $${{4\pi M\Ome...

In a photoelectric experiment a parallel beam of monochromatic light with power of $$200$$ $$W$$ is incident on a perfectly absorbing cathode of work ...

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for s...

The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioi...

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 2...

An $$\alpha$$-particle and a proton are accelerated from the rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $$\...

## MCQ (Single Correct Answer)

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.
[Given: Wien's constant...

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $6.0 \mathrm{~V...

A photoelectric material having work-function $${\phi _0}$$ is illuminated with light of wavelength $$\lambda \left( {\lambda < {{he} \over {{\phi...

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoel...

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to thes...

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is ...

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions $$\phi_p=2.0~\mathrm{eV}$$, $$\phi_...

The allowed energy for the particle for a particular value of $$n$$ is proportional to

If the mass of the particle is $$m=1.0\times10^{-30}$$ kg and $$a=6.6$$ nm, the energy of the particle in its ground state is closest to

## MCQ (More than One Correct Answer)

A heavy nucleus N, at rest, undergoes fission N $$\to$$ P + Q, where P and Q are two lighter nuclei. Let $$\delta$$ = MN $$-$$ MP $$-$$ MQ, where MP, ...

Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?

Light of wavelength $$\lambda$$ph falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $$...

For photo-electric effect with incident photon wavelength $$\lambda$$, the stopping potential is V0. Identify the correct variation(s) of V0 with $$\l...

Using the expression $$2d\sin \theta = \lambda $$, one calculates the values of d by measuring the corresponding angles $$\theta $$ in
the range 0 to...