The element ${}_{90}{}^{232}\mathrm{Th}$ belongs to thorium series. Which of the following will act as the end product of the series?

• ₈₂Pb²⁰⁸

• ₈₂Bi²⁰⁹

• ₈₂Pb²⁰⁶

• ₈₂Pb²⁰⁷

If radius of first Bohr's orbit of hydrogen atom is 'x', then the de-Broglie wavelength of electron in 3rd orbit is nearly

• 2πx

• 6πx

• 9x

• x/3

Which of the following notations shows the product incorrectly?

• ${}_5{}^{10}\mathrm{B} (\mathrm{\alpha }, \mathrm{n}) {}_7{}^{13}\mathrm{N}$

• ${}_{96}{}^{242}\mathrm{Cm} (\mathrm{\alpha }, 2\mathrm{n}) {}_{97}{}^{243}\mathrm{Bk}$

• ${}_7{}^{14}\mathrm{N} (\mathrm{n}, \mathrm{p}) {}_6{}^{14}\mathrm{C}$

• ${}_{14}{}^{28}\mathrm{Si} (\mathrm{d}, \mathrm{y}) {}_{15}{}^{30}\mathrm{P}$

Quantum numbers l = 2 and m= 0 represent the orbital

• d_xy

• d_x²-y²

• d_z²

• d_xz

The wavelength of associated wave of a particle moving with a speed of one-tenth that of light is 7Å. The particle must be

• electron

• proton

• nanoparticle

• photon

Which mathematical statement did not prove false?

• $∆\mathrm{E}= \mathrm{hv}$

• $\mathrm{R}=\frac{{\mathrm{me}}^4}{8{\mathrm{\epsilon }}_0^2{\mathrm{h}}^3\mathrm{c}}$

• $\mathrm{R}=\frac{{\mathrm{n}}_1^2{\mathrm{n}}_2^2\mathrm{v}}{({\mathrm{n}}_1^2-{\mathrm{n}}_2^2)\mathrm{c}}$

• $\mathrm{mvr}= \frac{\mathrm{nh}}{2\mathrm{\pi }}$

${}_{93}{}^{239}\mathrm{Np} \mathrm{is} \mathrm{a} \mathrm{\beta }- \mathrm{emitter}$, but the product is also radioactive and give ²³⁵U. Which particles(s) is/ are emitted by the product?

• 4 neutrons

• 4 protons

• 4 protons and 2electrons

• 2 neutrons and 2 protons

For a f-orbital, the values of m are

• -1, 0, +1

• 0, +1, +2, +3

• -2, -1, 0, +1, +2

• -3, -2, -1, 0, +1, +2, +3

A radio isotope will not emit

• gamma and alpha rays simultaneously

• gamma rays only

• alpha and beta rays simultaneously

• beta and gamma rays simultaneously

A lone pair of electrons in an atom implies

• a pair of valence electrons not involved in bonding

• a pair of electrons involved in bonding

• a pair of electrons

• a pair of valence electrons