The energy of an electron in the ground state | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -R_H \left( \frac{Z^2}{n^2} \right) \ J$. For $He^{+}$ ion,$Z

Vedclass · Accepted Answer

$-x$

Vedclass · Answer

(D) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -R_H \left( \frac{Z^2}{n^2} \right) \ J$. For $He^{+}$ ion,$Z=2$ and $n=1$: $E_1 = -R_H \left( \frac{2^2}{1^2} \right) = -4 R_H$. Given $E_1 = -x \ J$,we have $-4 R_H = -x$,which implies $R_H = \frac{x}{4}$. For $Be^{3+}$ ion,$Z=4$ and $n=2$: $E_2 = -R_H \left( \frac{4^2}{2^2} \right) = -R_H \left( \frac{16}{4} \right) = -4 R_H$. Substituting $R_H = \frac{x}{4}$ into the expression for $E_2$: $E_2 = -4 \left( \frac{x}{4} \right) = -x \ J$.

The energy of an electron in the ground state $(n=1)$ for $He^{+}$ ion is $-x \ J$. What is the energy for an electron in the $n=2$ state for $Be^{3+}$ ion in $J$?

Similar Questions

According to the Bohr theory,which of the following transitions in the hydrogen atom will give rise to the least energetic photon?

How does the energy of an orbit change as we move away from the nucleus in a hydrogen-like atom?

The radius of the fourth orbit in $He^{+}$ ion is '$R_1$' $pm$ and the radius of the third orbit in $Li^{2+}$ ion is '$R_2$' $pm$. The value of $(R_1 - R_2)$ in $pm$ is:

What is the ratio of the radius of the second Bohr orbit to the first Bohr orbit of the $H$ atom?

What is the maximum wavelength line in the Lyman series of $He^{+}$ ion?

Vedclass Test Series

Exam Paper Generator

Online Exam Module