If the half-life of a radioactive material is 10 years, then the percentage of the material decayed in 30 years is

The ratio of the time periods of the revolution of the electrons in the second and third excited states of hydrogen atom is

If the surface areas of two nucleii are in the ratio $9: 47$, then the ratio of their mass number is

The ratio of energies of photons produced due to transition of an electron in hydrogen atom from second energy level to first energy level and fifth energy level to second energy level is

The half life of a radioactive substance is 10 minutes. If $n_1$ and $n_2$ are the number of atoms decayed in 20 and 30 minutes respectively, then $n_1: n_2=$

The density (in $\mathrm{kg} \mathrm{m}^{-3}$ ) of nuclear matter is of the order of

Of the following, Bohr's atomic model is applicable to

The ratio of the orders of the spacings of nuclear energy levels and atomic energy levels is

The ratio of the wavelengths of the first Lyman line and the second Balmer line of hydrogen atom is

Each nuclear fission of ${ }^{235} \mathrm{U}$ releases 200 MeV of energy. If a reactor generates 1 MW power, then the rate of fission in the reactor is

The difference between the frequencies of second and first Paschen lines of hydrogen atom is ( $R=$ Rydberg constant and $c=$ speed of light in vacuum)

If the time taken for a radioactive substance to decay $8 \%$ to $77 \%$ is 12 minutes, then the half life of the substance in minutes is

For an observer on the Earth, if a spectral line of wavelength $6600\mathop {\rm{A}}\limits^{\rm{o}}$ emitted by a star is found to be red shifted by $22 \mathop {\rm{A}}\limits^{\rm{o}}$, then the star is

The difference between the frequencies of the first and second Lyman lines of hydrogen atom is ( $R=$ Rydberg constant and $c=$ speed of light in vacuum)

If the half-life of a radioactive element is 12.5 hours, then the time taken to disintegrate 256 g of the substance into 1 g is (in hours)

An element $X$ of a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. A sample is taken from a rock that contains both $X$ and $Y$ in the ratio $1: 7$. If at the time of formation of the rock $Y$ was not present in the sample, then the age of the rock in years is

Energy levels $A, B$ and $C$ of a certain atom corresponding to increasing values of energy i.e $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are the wavelengths of a photon corresponding to the transitions shown then.

The principle quantum number $n$ corresponding to the exited state of $\mathrm{He}^{+}$ion. If on transition to the ground state two photons in succession with wavelength $1026 \mathop {\rm{A}}\limits^{\rm{o}}$ and $304 \mathop {\rm{A}}\limits^{\rm{o}}$ are emitted $\left(R=1.097 \times 10^{-7} \mathrm{~m}^{-1}\right)$

The ratio of minimum wavelength of Balmer series to maximum wavelength in Brackett series in hydrogen spectrum is

The half-life period of a radioactive element $A$ is 62 years. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in 1:15 ratio. The age of the sample is

The speed of the electron in a hydrogen atom in the $n=3$ level is

(Planck's constant $=6.6 \times 10^{-34} \mathrm{Js}$ )

One mole of radium has an activity of $\frac{1}{3.7}$ kilo curie. Its decay constant is

(Avagadro number $=6 \times 10^{23} \mathrm{~mol}^{-1}$ )

An electron in the hydrogen atom excites from 2nd orbit to 4th orbit then the change in angular momentum of the electron is (Planck's constant $$h=6.64 \times 10^{-34} \mathrm{~J}-\mathrm{s}$$)

Choose the correct statement of the following

A ancient discovery found a sample, where $$75 \%$$ of the original carbon ($$\mathrm{C}^{14}$$) remains. Then the age of the sample is$$\binom{T_{\frac{1}{2}}\left(C^{14}\right)=5730 \text { years, } \ln 0.5=-0.7}{\ln (0.75)=-0.3}$$

A hydrogen atom at the ground level absorbs a photon and is excited n = 4 level. The potential energy of the electron in the excited state is

The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius 6 fermi is

Energy of a stationary electron in the hydrogen atom is $$E=\frac{13.6}{n^2} \mathrm{~eV}$$, then the energies required to excite the electron in hydrogen atom to (a) its second excited state and (b) ionised state, respectively.

The graph of $$\ln \left(\frac{R}{R_0}\right)$$ versus $\ln A$ is where $$R$$ is radius of a nucleus, $$A$$ is its mass number, and $$R_0$$ is constant

The shortest wavelength of X-rays emitted from an X-ray tube depends upon ........... .

The wavelength of the first spectral line ofthe Lyman series of hydrogen spectrum is

Which of the following nuclear reactions ispossible?

The angular momentum of the orbitalelectron is integral multiple of

Which of the following values is the correct order of nuclear density?

The ionisation potential of hydrogen atom is13.6 V. How much energy need to besupplied to ionise the hydrogen atom in thefirst excited state?

Which of the following statement is correct?

Potential energy between a proton and an electron is given by $$U=\frac{K e^2}{3 R^3}$$, then radius of Bohr's orbit can be given by