Explanation
Hint: For hydrogen atom, force on an electron due to nucleus is given by,
$$F = k\dfrac{{{e^2}}}{{{r^2}}}$$
Where,
$$k$$ is constant,
$$e$$ is charge on electron,
$$r$$ is distance of electron from nucleus.
Step 1: Note all the given values.
Formula for centripetal force for a particle of mass $$m$$ rotating with velocity $$v$$ in radius $$r$$ is given as,
$$F = \dfrac{{m{v^2}}}{r}$$
An electron revolving around a nucleus of the hydrogen atom. Force on the electron is given by,
This force acts as centripetal force on electron responsible for rotation.
Thus,
$$k\dfrac{{{e^2}}}{{{r^2}}} = \dfrac{{m{v^2}}}{r}$$
$$ \Rightarrow v = \sqrt {\dfrac{{k{e^2}}}{{mr}}} $$
Step 2: Find an expression for Angular Momentum.
Now, Angular momentum of electron is given as,
$$L = mvr$$
$$ \Rightarrow L = mr\sqrt {\dfrac{{k{e^2}}}{{mr}}} $$
$$ \Rightarrow L = \sqrt {mrk{e^2}} $$
Since m r k are constants.
$$ \Rightarrow L \propto \sqrt r $$
Thus, the angular momentum of an electron in a hydrogen atom is proportional to the square root of the distance of the electron from the nucleus.
Fluorescence is the emission of light by a substance that as absorbed light as other electromagnetic radiation. It occurs due to presence of phosphorous in the metal tube. Because phosphorous is a material that glows when exposed to electrical energy. Because actual conversion of electrical to light energy takes place on display screen when electron strike phosphorous.
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