Energy and radius of the first Bohr orbit of $He^+$ and <span class=...

Hint : $r_n=0.529 \dfrac{n^2}{Z}$ Explanation : 1. $He^+ $ (Helium ion, Z=2): $r_1=\frac{a_0}{Z}=\frac{52.9}{2}=26.45 \mathrm{pm}$ (approx. 26.4 pm as listed) $E_1=-\frac{2.18 \times 10^{-18} \times 2^2}{1^2}=-8.72 \times 10^{-18} \mathrm{~J} \text { (approx. }-8.72 \times 10^{-18} \mathrm{~J}$ as listed, though the table shows $-19.62 \times 10^{-18} \mathrm{~J} \text { for } n=1 \text {, }$ which may be a typo or context-specific adjustment) 2. $Li^{2+}$ (Lithium ion, Z=3 $r_1=\frac{52.9}{3} \approx 17.63 \mathrm{pm}$ (approx. 17.6 pm is listed) $E_1=-\frac{2.18 \times 10^{-18} \times 3^2}{1^2}=-19.62 \times 10^{-18} \mathrm{~J}$ (matches the table value)

Bohrs Theory - NEET Chemistry PYQs

Q: Energy and radius of the first Bohr orbit of $He^+$ and <span class=...

Hint : $r_n=0.529 \dfrac{n^2}{Z}$ Explanation : 1. $He^+ $ (Helium ion, Z=2): $r_1=\frac{a_0}{Z}=\frac{52.9}{2}=26.45 \mathrm{pm}$ (approx. 26.4 pm as listed) $E_1=-\frac{2.18 \times 10^{-18} \times 2^2}{1^2}=-8.72 \times 10^{-18} \mathrm{~J} \text { (approx. }-8.72 \times 10^{-18} \mathrm{~J}$ as listed, though the table shows $-19.62 \times 10^{-18} \mathrm{~J} \text { for } n=1 \text {, }$ which may be a typo or context-specific adjustment) 2. $Li^{2+}$ (Lithium ion, Z=3 $r_1=\frac{52.9}{3} \approx 17.63 \mathrm{pm}$ (approx. 17.6 pm is listed) $E_1=-\frac{2.18 \times 10^{-18} \times 3^2}{1^2}=-19.62 \times 10^{-18} \mathrm{~J}$ (matches the table value)

Energy and radius of the first Bohr orbit of

He%5E%2B

and

Li%5E%7B2%2B%7D

are :
[Given

%5Cleft.%5Cmathrm%7BR%7D_%7B%5Cmathrm%7BH%7D%7D%3D2.18%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D%2C%20%5Cmathrm%7Ba%7D_0%3D52.9%20%5Cmathrm%7Bpm%7D%5Cright%5D

1.	$%5Cbegin%7Baligned%7D%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D-19.62%20%5Ctimes%2010%5E%7B-16%7D%20%5Cmathrm%7B~J%7D%20%3B%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D17.6%5Cmathrm%7Bpm%7D%20%5C%5C%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D8.72%20%5Ctimes%2010%5E%7B-16%7D%20%5Cmathrm%7B~J%7D%20%3B%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D26.4%20%5Cmathrm%7Bpm%7D%20%5Cend%7Baligned%7D$
2.	$%5Cbegin%7Baligned%7D%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D-8.72%20%5Ctimes%2010%5E%7B-16%7D%20%5Cmathrm%7B~J%7D%20%3B%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D17.6%20%5Cmathrm%7Bpm%7D%20%5C%5C%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D-19.62%20%5Ctimes%2010%5E%7B-16%7D%20%5Cmathrm%7B~J%7D%20%3B%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D17.6%20%5Cmathrm%7Bpm%7D%20%5Cend%7Baligned%7D$
3.	$%5Cbegin%7Baligned%7D%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D-%2019.62%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D17.6%20%5Cmathrm%7Bpm%7D%20%5C%5C%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D-8.72%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D26.4%20%5Cmathrm%7Bpm%7D%20%5Cend%7Baligned%7D$
4.	$%5Cbegin%7Baligned%7D%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D-8.72%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BLi%7D%5E%7B2%2B%7D%5Cright)%3D26.4%20%5Cmathrm%7Bpm%7D%20%5C%5C%20%26%20%5Cmathrm%7BE%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D-19.62%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D%20%3B%20%5C%5C%20%26%20%5Cmathrm%7Br%7D_%7B%5Cmathrm%7Bn%7D%7D%5Cleft(%5Cmathrm%7BHe%7D%5E%7B%2B%7D%5Cright)%3D17.6%20%5Cmathrm%7Bpm%7D%20%5Cend%7Baligned%7D$

Hint:

r_n%3D0.529%20%5Cdfrac%7Bn%5E2%7D%7BZ%7D

Explanation:
1.

He%5E%2B

(Helium ion, Z=2):

r_1%3D%5Cfrac%7Ba_0%7D%7BZ%7D%3D%5Cfrac%7B52.9%7D%7B2%7D%3D26.45%20%5Cmathrm%7Bpm%7D

(approx. 26.4 pm as listed)

E_1%3D-%5Cfrac%7B2.18%20%5Ctimes%2010%5E%7B-18%7D%20%5Ctimes%202%5E2%7D%7B1%5E2%7D%3D-8.72%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D%20%5Ctext%20%7B%20(approx.%20%7D-8.72%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D

as listed, though the table shows

-19.62%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D%20%5Ctext%20%7B%20for%20%7D%20n%3D1%20%5Ctext%20%7B%2C%20%7D

which may be a typo or context-specific adjustment)
2.

Li%5E%7B2%2B%7D

(Lithium ion, Z=3

r_1%3D%5Cfrac%7B52.9%7D%7B3%7D%20%5Capprox%2017.63%20%5Cmathrm%7Bpm%7D

(approx. 17.6 pm is listed)

E_1%3D-%5Cfrac%7B2.18%20%5Ctimes%2010%5E%7B-18%7D%20%5Ctimes%203%5E2%7D%7B1%5E2%7D%3D-19.62%20%5Ctimes%2010%5E%7B-18%7D%20%5Cmathrm%7B~J%7D

(matches the table value)

Bohrs Theory

High-Yield Trend

Questions
5 MCQs

Official Solution

Official Solution

Official Solution

Official Solution

Official Solution

1.	Larger the value of n, the larger the orbit radius.
2.	Equation can be used to calculate the change in energy when the electron changes orbit.
3.	For n = 1, the electron has a more negative energy than it does for n = 6 which means that the electron is more loosely bound in the smallest allowed orbit.
4.	The negative sign in the equation simply means that the energy of the electron bound to the nucleus is lower than what it would be if the electrons were at an infinite distance from the nucleus.

1.	$-%5Cdfrac%20x9$	2.	$-4x$
3.	$-%5Cdfrac%2049x$	4.	$-x$

Bohrs Theory

High-Yield Trend

Questions 5 MCQs

Official Solution

Official Solution

Official Solution

Official Solution

Official Solution

Questions
5 MCQs