Respuesta :
Explanation:
It is given that the atom is hydrogen. And, its electron rotates in n = 5 orbit with angular speed [tex]3.3 \times 10^{14} rad/s[/tex].
Radius of circular path = [tex]1.32 \times 10^{-9}[/tex] m
Hence, first calculate the tangential speed as follows.
Tangential speed = radius × angular speed
= [tex]4.356 \times 10^{5} m/s[/tex]
As formula to calculate time period is as follows.
T = [tex]1.5211 \times 10^{-16} \times \frac{n^{3}}{z^{2}}[/tex] sec
Also, frequency [tex](\nu)[/tex] = [tex]\frac{1}{T}[/tex]
So, for n = 5 and z = 1 the value of frequency is as follows.
frequency [tex](\nu)[/tex] = [tex]\frac{1}{1.5211 \times 10^{-16}} \times \frac{z^{2}}{n^{3}}[/tex]
= [tex]\frac{1}{1.5211 \times 10^{-16}} \times \frac{1}{(5)^{3}}[/tex]
= [tex]5.259 \times 10^{13}[/tex] Hz
As formula to calculate centripetal acceleration is as follows.
[tex]a_{c} = \frac{v^{2}}{r}[/tex]
where, v = linear speed
r = radius
v = [tex]2.165 \times 10^{6} \times \frac{z}{n}[/tex]
= [tex]2.165 \times 10^{6} \times \frac{1}{5}[/tex]
= [tex]4.3 \times 10^{5} m/s[/tex]
Hence, the centripetal acceleration will be as follows.
[tex]a_{c} = \frac{v^{2}}{r}[/tex]
= [tex]\frac{(4.3 \times 10^{5})^{2}}{1.32 \times 10^{-9}}[/tex]
= [tex]1.4 \times 10^{20} m/s^{2}[/tex]
Thus, we can conclude that the electron's centripetal acceleration is [tex]1.4 \times 10^{20} m/s^{2}[/tex].
