Question

Calculate the radius of the 3rd orbit of an atom with 1 proton and 2 neutrons.

Answer 1

Let's consider the formula of the radius n-th Bohr orbit:

$R_{n} = \frac{1}{\pi}\frac{\epsilon_{0}}{Ze^{2}}\frac{n^{2}h^2}{m_e}$

where: $h$ - Planck's constant

$\epsilon_0$ - the vacuum dielectric constant

$m_e$ - the mass of electron

$e$ - the charge of the electron\proton

$Z$ - numder of protons in the nucleus

As we can see the radius doesn't depend from the mass of the nucleus. In this way, the radius depends from the number of protons in our nucleus. Hence, the answer on this problem:

$R_3 = \frac{1}{\pi}\frac{\epsilon_{0}}{e^{2}}\frac{9h^2}{m_e}$