Answer:
![4.86\times10^{-7}\ \text{m}](https://tex.z-dn.net/?f=4.86%5Ctimes10%5E%7B-7%7D%5C%20%5Ctext%7Bm%7D)
Explanation:
R = Rydberg constant = ![1.09677583\times 10^7\ \text{m}^{-1}](https://tex.z-dn.net/?f=1.09677583%5Ctimes%2010%5E7%5C%20%5Ctext%7Bm%7D%5E%7B-1%7D)
= Principal quantum number of an energy level = 2
= Principal quantum number of an energy level for the atomic electron transition = 4
Wavelength is given by the Rydberg formula
![\lambda^{-1}=R\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)\\\Rightarrow \lambda^{-1}=1.09677583\times 10^7\left(\dfrac{1}{2^2}-\dfrac{1}{4^2}\right)\\\Rightarrow \lambda=\left(1.09677583\times 10^7\left(\dfrac{1}{2^2}-\dfrac{1}{4^2}\right)\right)^{-1}\\\Rightarrow \lambda=4.86\times10^{-7}\ \text{m}](https://tex.z-dn.net/?f=%5Clambda%5E%7B-1%7D%3DR%5Cleft%28%5Cdfrac%7B1%7D%7Bn_1%5E2%7D-%5Cdfrac%7B1%7D%7Bn_2%5E2%7D%5Cright%29%5C%5C%5CRightarrow%20%5Clambda%5E%7B-1%7D%3D1.09677583%5Ctimes%2010%5E7%5Cleft%28%5Cdfrac%7B1%7D%7B2%5E2%7D-%5Cdfrac%7B1%7D%7B4%5E2%7D%5Cright%29%5C%5C%5CRightarrow%20%5Clambda%3D%5Cleft%281.09677583%5Ctimes%2010%5E7%5Cleft%28%5Cdfrac%7B1%7D%7B2%5E2%7D-%5Cdfrac%7B1%7D%7B4%5E2%7D%5Cright%29%5Cright%29%5E%7B-1%7D%5C%5C%5CRightarrow%20%5Clambda%3D4.86%5Ctimes10%5E%7B-7%7D%5C%20%5Ctext%7Bm%7D)
The wavelength of the light emitted is
.
Explanation:
It is known that for a body centered cubic unit cell there are 2 atoms per unit cell.
This means that volume occupied by 2 atoms is equal to volume of the unit cell.
So, according to the volume density
![5 \times 10^{26} atoms = 1 [tex]m^{3}](https://tex.z-dn.net/?f=5%20%5Ctimes%2010%5E%7B26%7D%20atoms%20%3D%201%20%5Btex%5Dm%5E%7B3%7D)
2 atoms = ![\frac{1 m^{3}}{5 \times 10^{26} atoms} \times 2 atoms](https://tex.z-dn.net/?f=%5Cfrac%7B1%20m%5E%7B3%7D%7D%7B5%20%5Ctimes%2010%5E%7B26%7D%20atoms%7D%20%5Ctimes%202%20atoms)
= ![4 \times 10^{-27} m^{3}](https://tex.z-dn.net/?f=4%20%5Ctimes%2010%5E%7B-27%7D%20m%5E%7B3%7D)
Formula for volume of a cube is
. Therefore,
Volume of the cube = ![4 \times 10^{-27} m^{3}](https://tex.z-dn.net/?f=4%20%5Ctimes%2010%5E%7B-27%7D%20m%5E%7B3%7D)
As lattice constant (a) = ![(4 \times 10^{-27} m^{3})^{\frac{1}{3}}](https://tex.z-dn.net/?f=%284%20%5Ctimes%2010%5E%7B-27%7D%20m%5E%7B3%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
= ![1.59 \times 10^{-9} m](https://tex.z-dn.net/?f=1.59%20%5Ctimes%2010%5E%7B-9%7D%20m)
Therefore, the value of lattice constant is
.
And, for bcc unit cell the value of radius is as follows.
r = ![\frac{\sqrt{3}}{4}a](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7Da)
Hence, effective radius of the atom is calculated as follows.
r = ![\frac{\sqrt{3}}{4}a](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7Da)
= ![\frac{\sqrt{3}}{4} \times 1.59 \times 10^{-9} m](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D%20%5Ctimes%201.59%20%5Ctimes%2010%5E%7B-9%7D%20m)
= ![6.9 \times 10^{-10} m](https://tex.z-dn.net/?f=6.9%20%5Ctimes%2010%5E%7B-10%7D%20m)
Hence, the value of effective radius of the atom is
.
The average melting point for a solid is -38.83 degrees Celsius and -37.89 degrees Fahrenheit.<span />
The fourth (last) one in 2-8-8-2.