Which of the following relations is correct f | vedclass

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(B) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.For the ground state

Vedclass · Accepted Answer

$E_1(H) = E_2(He^+) = E_3(Li^{2+}) = E_4(Be^{3+})$

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(B) The energy of an electron in a hydrogen-like species is given by the formula: $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.For the ground state of $H$ $(Z=1, n=1)$: $E_1 = -13.6 	imes \frac{1^2}{1^2} = -13.6 	ext{ eV}$.For the $n=2$ state of $He^+$ $(Z=2, n=2)$: $E_2 = -13.6 	imes \frac{2^2}{2^2} = -13.6 	ext{ eV}$.For the $n=3$ state of $Li^{2+}$ $(Z=3, n=3)$: $E_3 = -13.6 	imes \frac{3^2}{3^2} = -13.6 	ext{ eV}$.For the $n=4$ state of $Be^{3+}$ $(Z=4, n=4)$: $E_4 = -13.6 	imes \frac{4^2}{4^2} = -13.6 	ext{ eV}$.Thus,$E_1(H) = E_2(He^+) = E_3(Li^{2+}) = E_4(Be^{3+})$.

$(P). \lambda_{\max }$ in Lyman series	$(i). \infty \rightarrow 1$
$(Q). v_{\min }$ in Balmer series	$(ii). 2 \rightarrow 1$
$(R). \lambda_{\min }$ in Lyman series	$(iii). 3 \rightarrow 2$
$(S). v_{\max }$ in Balmer series	$(iv). \infty \rightarrow 2$

Which of the following relations is correct for the energy of the ground state of hydrogen-like species?

Similar Questions

When the electron of a hydrogen atom returns to the $L$ shell $(n=2)$ from shells of higher energy,we get a series of lines in the spectrum. This series is called:

Match the following for hydrogen atom $(Z=1)$ :-
$(P). \lambda_{\max }$ in Lyman series $(i). \infty \rightarrow 1$
$(Q). v_{\min }$ in Balmer series $(ii). 2 \rightarrow 1$
$(R). \lambda_{\min }$ in Lyman series $(iii). 3 \rightarrow 2$
$(S). v_{\max }$ in Balmer series $(iv). \infty \rightarrow 2$

Explain the following according to Bohr's model of hydrogen:
$(i)$ Principal quantum number
$(ii)$ Radius of stationary orbit $(r)$
$(iii)$ Energy of stationary state
$(iv)$ Isoelectronic ion of $H$
$(v)$ Velocity of electron

Find the wavelength of the third line in the Brackett series of the hydrogen spectrum.

When an electron in a hydrogen atom jumps from an infinite state to the first stationary state,the wavelength of the emitted radiation will be ...... (Rydberg constant = $1.097 \times 10^7 \ m^{-1}$):

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