Explanation
The angular momentum of $$\alpha$$ particles is conserved because there is no external torque.
Hint:
Number of Photons emitted by H-atom if it is excited to $${n^{th}}$$ excited state is,
$$\bf{photons = \dfrac{{n(n - 1)}}{2}}$$
Step 1: Calculate the number of photons emitted by H-atom
Hydrogen atom is excited to $${4^{th}}$$ excited state, so number of photons emitted by using formula is,
$$photons = \dfrac{{n(n - 1)}}{2}$$
$$ \Rightarrow photons = \dfrac{{4(4 - 1)}}{2}$$
$$ \Rightarrow photons = 6$$
Thus, 6 photons are emitted if the Hydrogen atom is excited to $${4^{th}}$$ excited state.
Option B is correct.
For an atom of atomic number Z, The radius of $${n^{th}}$$ orbit is given as,
$${r_n} = \dfrac{{{n^2}{a_o}}}{Z}$$
Where, $${a_o}$$ is Bohr’s radius, $${a_o} = 53pm$$
Correct Option : Option D.
Explanation for correct answer:
a) $${_1^1}H$$
$$Z = 1$$
For shortest orbit, $$n = 1$$
Therefore, $${r_1} = \dfrac{{{1^2} \times 53}}{1} = 53pm$$
b) $${_2^1}H$$
c) $$H{e^ + }$$
$$Z = 2$$
Therefore, $${r_1} = \dfrac{{{1^2} \times 53}}{2} = 26.5pm$$
d) $$L{i^ + }$$
$$Z = 3$$
Therefore, $${r_1} = \dfrac{{{1^2} \times 53}}{3} = 17.667pm$$
The radius of shortest orbit of $$L{i^ + }$$ is closest to $$18pm$$. Thus Option D is the correct answer.
The ratio of momenta of an electron and a $$\alpha$$ -particle which is accelerated from rest by a potential difference of $$100 V$$ is:
Hint: The Rutherford alpha particle scattering experiment showed that most of the space of the atom is empty
Explanation: The Rutherford alpha particle scattering experiment has the following observation: 1. Most of the alpha particle remains undeflected that means most of the space was empty and the particles came undeflected by positive charges in the atom. It was a very small portion and termed as the nucleus.
2. Some of the alpha particles show a small deviation from the original path.
3. Very few particles bounced backSo, Conclusions can be made from this as;
1. Most of the space in the atom remains empty.
2. And a large amount of mass is concentrated in the small space called a nucleus.
Final answer: The correct answer is $$C$$.
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