Embibe Experts Solutions for Chapter: Structure of Atom, Exercise 2: Level 2

A bulb of $40 \mathrm{W}$ is producing a light of wavelength $620 \mathrm{nm}$ with $80 \%$ of efficiency, then the number of photons emitted by the bulb in $20$ seconds are: $\left(1 \mathrm{eV}=1.6\times {10}^{-19} \mathrm{J}, \mathrm{hc}=12400 \mathrm{eV} \mathrm{\AA })\right.$

The frequency of radiation emitted when the electron falls from $\mathrm{n}=4$ to $\mathrm{n}=1$ in a hydrogen atom will be (given ionization energy of $\mathrm{H}=2.18\times {10}^{-18}\mathrm{J} {\mathrm{atom}}^{-1}$ and $\mathrm{h}=6.625\times {10}^{-34} \mathrm{J} \mathrm{s}$).

Calculate the wavelength in nanometer associated with a proton moving at $1.0\times {10}^3\mathrm{meter} {\mathrm{second}}^{-1}. \left(\text{Mass of proton }=1.67\times {10}^{-27}\mathrm{kilogram}\mathrm{and}\mathrm{h}=6.63\times {10}^{-34}\mathrm{Joule} \mathrm{second}\right)$

In an atom, an electron is moving with a speed of $600 \mathrm{m}/\mathrm{s}$ with an accuracy of $0.005\%$. Certainty with which the position of the electron can be located is,$\left(\mathrm{h}=6.6\times {10}^{-34} \mathrm{kg} {\mathrm{m}}^2{\mathrm{s}}^{-1}\mathrm{,} {\mathrm{m}}_{\mathrm{e}}=9.1\times {10}^{-31} \mathrm{kg}\right)$

In Bohr theory, if ${\mathrm{E}}_{{\mathrm{n}}^{\text{'}}}{\mathrm{K}}_{{\mathrm{n}}^{\text{'}}}{\mathrm{V}}_{\mathrm{n}}$ and ${\mathrm{r}}_{\mathrm{n}}$ denotes total energy, kinetic energy, potential energy and radius of ${\mathrm{n}}^{\mathrm{th}}$ orbit respectively, which of the following is (are) correct?

If first ionization potential of a hypothetical atom is $16 \mathrm{V},$ then the first excitation potential will be:

In an experiment to measure the charge on an electron, the following values of charge were found on the oil droplets: $-1.6\times {10}^{-19} ,-2.4\times {10}^{-19} ,-4.0\times {10}^{-19}$ (in coulomb).

What values of the electric charge would be indicated by these results? If the answer is of form $-\mathrm{y}\times {10}^{-19}$, report the value of $\mathrm{y}$.

An electron beam can undergo diffraction by crystals. Through what potential should a beam of electrons be accelerated so that its wavelength becomes equal to $1.54 \mathrm{\AA }$? Values of ${\mathrm{m}}_e=9.1\times {10}^{-31 }\mathrm{kg}$ and $\mathrm{h}=6.62\times {10}^{-34} \mathrm{J}.\mathrm{s}$.

Give answer after multiplying with 10 and rounding off to the nearest integer value.