Atoms and Nuclei

A radioactive element ${ }_{92}^{242} \mathrm{X}$ emits two $\alpha$－particles，one electron and two positrons．The transformed nucleus is represented by ${ }_P^{234} Y$ ．The value of $P$ is

The de-Broglie wavelength of an electron in 4th orbit is (where $r=$ radius of the 1st orbit)

The number of undecayed nuclei $N$ in a sample of radioactive material as a function of time $(t)$ is shown in the figure. Which of the following graphs correctly show the relationship between $N$ and the activity ' $A$ '?

Let the binding energy per nucleon of nucleus is denoted by ' $E_{b n}$ ' and radius of the nucleus is denoted by ' $r$ '. If mass number of nuclei $A$ and $B$ are 64 and 125 respectively, then

The minimum wavelength of Lyman series lines is $P$, then the maximum wavelength of these lines is

A radioactive nucleus decays as follows :
\(X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4\)
If the mass number and atomic number of ' $X_4$ ' are 172 and 69 respectively, then the ato...

Which of the following statement(s) is/are truc in respect of nuclear binding energy ?
(i) The mass energy of a nucleus is larger than the total mass energy of its individual protons and neutrons.
(ii) If a nucleus could be separated into i...

A uniform magnetic field B exists in a region. An electron of charge q and mass m moving with velocity v enters the region in a direction perpendicular to the magnetic field. Considering Bohr angular momentum quantization, which of the foll...

If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of n = \(\infty\) state is,

A sample of hydrogen atom in its ground state is radiated with photons of 10.2 eV energies. The radiation from the sample is absorbed by excited ionized He+. Thenwhich of the following statement/s is/are true?

Suppose in a hypothetical world the angular momentum is quantized to be even integral multiples of \({h \over {2\pi }}\). The largest possible wavelength emitted by hydrogen atoms in visible range in a world according to Bohr's model will b...

If the kinetic energies of an electron, an alpha particle and a proton having same de-Broglie wavelength are \({\varepsilon _1},{\varepsilon _2}\) and \({\varepsilon _3}\) respectively, then

Let r, v, E be the radius of orbit, speed of electron and total energy of electron respectively in H-atom. Which of the following quantities according to Bohr theory, is proportional to the quantum number n ?

A 12.5 eV electron beam is used to bombard gaseous hydrogen at ground state. The energy level upto which the hydrogen atoms would be excited is

If R is the Rydberg constant in cm-1, then hydrogen atom does not emit any radiation of wavelength in the range of

For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV, respectively. If a nucleus of mass number 238 breaks into two nuclei of nearly equal masses, what will be the approxim...

A nucleus X emits a \(\beta\)-particle to produce a nucleus Y. If their atomic masses are Mx and My respectively, then the maximum energy of the \(\beta\)-particle emitted is (where, me is the mass of an electron and c is the velocity of ...

A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2000 times heavier than an electron, what will be the relation between the de Broglie wavelength of the proton ($$\lambda...

A parent nucleus X undergoes \(\alpha\)-decay with a half-life of 75000 yrs. The daughter nucleus Y undergoes \(\beta\)-decay with a half-life of 9 months. In a particular sample, it is found that the rate of emission of \(\beta\)-particles...

To which of the following the angular velocity of the electron in the n-th Bohr orbit is proportional?

If the half-life of a radioactive nucleus is 3 days, nearly what fraction of the initial number of nuclei will decay on the third day? (Given, \(\root 3 \of {0.25} \approx 0.63\))

An electron accelerated through a potential of 10000 V from rest has a de-Broglie wave length \(\lambda\). What should be the accelerating potential, so that the wavelength is doubled?

How the linear velocity v of an electron in the Bohr orbit is related to its quantum number n?

Radon-222 has a half-life of 3.8 days. If one starts with 0.064 kg of radon-222 left after 19 days will be

Let vn and En be the respective speed and energy of an electron in the nth orbit of radius rn, in a hydrogen atom, as predicted by Bohr's model. Then

The de-Broglie wavelength of an electron is \(0.4 \times {10^{ - 10}}\) m when its kinetic energy is 1.0 keV. Its wavelength will be \(1.0 \times {10^{ - 10}}\) m, when its kinetic energy is

The wavelength of second Balmer line in hydrogen spectrum is 600 nm. The wavelength for its third line in Lyman series is

Which of the following statements is correct?

The ionisation potential of hydrogen atom is \(-\)13.6 eV. An electron in the ground state of a hydrogen atom absorbs a photon of energy 12.75 eV. How many different spectral lines can one expect when the electron make a downward transition...