Atoms and Nuclei · Physics · MHT CET (Biology)

In the Bohr model of hydrogen atom, out of the following quantities, the principal quantum number is proportional to ( $\mathrm{R}, \mathrm{V}$ and E represent radius of the orbit, speed of electron and total energy of the electron respectively)

According to Bohr's first postulate the kinetic energy $\frac{1}{2} m v^2$ of the electron in C.G.S. system is ( $\mathrm{m}=$ mass of electron, v is its velocity, r is the radius of the stationary orbit around the nucleus with charge Ze )

In the spectrum of hydrogen atom the ratio of the longest wavelength in the Balmer series to the longest wavelength in the Lyman series is

The series limit for the frequency of Balmer series is ' $\mathrm{v}_{\mathrm{B}}$ ', then the series limit frequency of Paschen series ' $v_p$ ' is

Radioactive materials A and B have decay constants ' $9 \lambda$ ' and ' $\lambda$ ' respectively. Initially they have same number of nuclei. The ratio of number of nuclei of material ' $A$ ' to that of ' $B$ ' will be $\left(\frac{1}{\mathrm{e}}\right)$ after time ' $t$ '. So ' $t$ ' is equal to

If $R_1$ and $R_2$ are the radii of the atomic nuclei of mass numbers 27 and 125 respectively, then the ratio $R_2: R_1$ is

The angular momentum of electron in hydrogen atom in first orbit is ' $L$ '. The change in angular momentum if electron is in second orbit of hydrogen atom is

If an electron in hydrogen atom jumps from $3^{\text {rd }}$ orbit to $2^{\text {nd }}$ orbit it emits a photon of wavelength ' $\lambda$ '. When it emits a photon from $4^{\text {th }}$ orbit to $3^{\text {rd }}$ orbit then the corresponding wavelength of emitted photon will be