JEE Advanced · 2021 · 03 Oct 2021 · Paper 1 · Modern Physics

Consider a hydrogen atom with ${\mathrm{v}}_{\mathrm{k}},{\mathrm{r}}_{\mathrm{k}}$ and ${\mathrm{K}}_{\mathrm{k}}$ denoting the velocity, orbital radius and kinetic energy of the electron in the $k^{\text{th }}$ orbit, respectively. The electron undergoes a transition from the …

A nuclear reactor starts producing a radioactive nuclide $X$ from $t=0$, at a constant rate of $\alpha$ per second. Each decay of $X$ produces energy $E_0$, which is utilized to heat a liquid of mass $m$ and specific heat $s$. Assuming no heat loss from the liquid …

Consider an electron in the $n=3$ orbit of a hydrogen-like atom with atomic number $Z$. At absolute temperature $T$, a neutron having thermal energy $k_{\mathrm{B}}T$ has the same de Broglie wavelength as that of this electron. If this temperature is given by …

List-I shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-II.
Choose the option that describes the correct match between the entries in List-I to those in List-II.

| List-I | | List- …

A hydrogen atom, initially at rest in its ground state, absorbs a photon of frequency $v_1$ and ejects the electron with a kinetic energy of 10 eV. The electron then combines with a positron at rest to form a positronium atom in its ground state and simultaneously emits a pho …

A particle of mass $m$ is moving in a circular orbit under the influence of the central force $\mathrm{F}(r)=-kr$, corresponding to the potential energy $V(r)=k{r}^2/2$, where $k$ is a positive force constant and $r$ is the radial distance from the origin. According …