Answer:
K.E. = 5.4362 × 10⁻¹⁹ J
Explanation:
The expression for Bohr velocity is:
[tex]v=\frac{Ze^2}{2 \epsilon_0\times n\times h}[/tex]
Applying values for hydrogen atom,
Z = 1
Mass of the electron ([tex]m_e[/tex]) is 9.1093×10⁻³¹ kg
Charge of electron (e) is 1.60217662 × 10⁻¹⁹ C
[tex]\epsilon_0[/tex] = 8.854×10⁻¹² C² N⁻¹ m⁻²
h is Plank's constant having value = 6.626×10⁻³⁴ m² kg / s
We get that:
[tex]v=\frac {2.185\times 10^6}{n}\ m/s[/tex]
Given, n = 2
So,
[tex]v=\frac {2.185\times 10^6}{2}\ m/s[/tex]
[tex]v=1.0925\times 10^6\ m/s[/tex]
Kinetic energy is:
[tex]K.E.=\frac {1}{2}\times mv^2[/tex]
So,
[tex]K.E.=\frac {1}{2}\times 9.1093\times 10^{-31}\times ({1.0925\times 10^6})^2[/tex]
K.E. = 5.4362 × 10⁻¹⁹ J
