(C) The radius of the $n^{th}$ Bohr orbit is given by the formula: $r_n = 0.529 \times \frac{n^2}{Z} \ \mathring{A}$. For the first Bohr orbit,$n = 1

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$r_{H} > r_{He^{+}} > r_{Li^{2+}}$

(C) The radius of the $n^{th}$ Bohr orbit is given by the formula: $r_n = 0.529 \times \frac{n^2}{Z} \ \mathring{A}$. For the first Bohr orbit,$n = 1$,so $r \propto \frac{1}{Z}$,where $Z$ is the atomic number. The atomic numbers are: $Z_H = 1$,$Z_{He^{+}} = 2$,and $Z_{Li^{2+}} = 3$. Since the radius is inversely proportional to the atomic number $(Z)$,a higher atomic number results in a smaller radius. Therefore,the order of radii is $r_H > r_{He^{+}} > r_{Li^{2+}}$.

Class 11 Chemistry Structure of Atom Atomic models and Planck's quantum theory

Medium

The radii of the first Bohr orbit of $H$ $(r_{H})$,$He^{+}$ $(r_{He^{+}})$ and $Li^{2+}$ $(r_{Li^{2+}})$ are in the order

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A
$r_{He^{+}} > r_{H} > r_{Li^{2+}}$
B
$r_{H} < r_{He^{+}} < r_{Li^{2+}}$
C
$r_{H} > r_{He^{+}} > r_{Li^{2+}}$
D
$r_{Li^{2+}} > r_{H} > r_{He^{+}}$

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Structure of Atom

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Atomic models and Planck's quantum theory

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The radii of the first Bohr orbit of $H$ $(r_{H})$,$He^{+}$ $(r_{He^{+}})$ and $Li^{2+}$ $(r_{Li^{2+}})$ are in the order

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Find the energy of $1$ mole of photons having a frequency of $5 \times 10^{10} \ s^{-1}$. $(h = 6.62 \times 10^{-34} \ J \ s)$

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Find the energy of each of the photons which:
$(i)$ correspond to light of frequency $3 \times 10^{15} \, Hz$
$(ii)$ have a wavelength of $0.50 \, \mathring{A}$

The kinetic energy of electrons emitted,when radiation of frequency $1.0 \times 10^{15} \ Hz$ hits a metal,is $2 \times 10^{-19} \ J$. What is the threshold frequency of the metal (in $Hz$)?
$(h = 6.6 \times 10^{-34} \ Js)$