Which of the following statements are correct | vedclass

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

Question

(B) $I$) The energy of the hydrogen atom in its ground state $(n=1)$ is given by $E_n = -13.6 \ eV / n^2$. For $n=1$,$E_1 = -13.6 \ eV$. Thus,statemen

Vedclass · Accepted Answer

$I$ & $III$ only

Vedclass · Answer

(B) $I$) The energy of the hydrogen atom in its ground state $(n=1)$ is given by $E_n = -13.6 \ eV / n^2$. For $n=1$,$E_1 = -13.6 \ eV$. Thus,statement $I$ is correct.$II$) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by $r_n = 52.9 	imes n^2 / Z \ pm$. For $H$ $(Z=1)$ and $n=3$,$r_3 = 52.9 	imes 3^2 / 1 = 476.1 \ pm$. Thus,statement $II$ is incorrect.$III$) The radius of the first orbit $(n=1)$ is $r_1 = 52.9 	imes (1^2 / Z) \ pm$. As $Z$ increases,$r_1$ decreases. The atomic numbers are $H(1), He^{+}(2), Li^{2+}(3), Be^{3+}(4)$. Therefore,the order of radii is $H > He^{+} > Li^{2+} > Be^{3+}$. Thus,statement $III$ is correct.Conclusion: $I$ and $III$ are correct.

Similar Questions

$A$ bulb emits light of wavelength $4500 \ \mathring{A}$. The bulb is rated at $150 \ \text{W}$ and $8\%$ of the energy is emitted as light. How many photons are emitted by the bulb per second?

The energy required to excite an electron from the first orbit to the third orbit in a hydrogen atom is .......... $eV$.

$A$ $100 \, W$ bulb emits monochromatic light of wavelength $400 \, nm$. Calculate the number of photons emitted per second by the bulb.

Calculate the ratio of the radius of the $2^{nd}$ and $3^{rd}$ orbit of a hydrogen atom. (Note: $r_n \propto n^2$)

Heat treatment of muscular pain involves radiation of wavelength of about $900 \ nm$. Which spectral line of $H$ atom is suitable for this purpose?
$[R_H = 1.097 \times 10^7 \ m^{-1}, \ h = 6.626 \times 10^{-34} \ J \cdot s, \ c = 3 \times 10^8 \ m/s]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module