Complete Question
The complete question is shown on the first uploaded image
Answer:
The value of n is 
Explanation:
From the question we are told that
The value of m = 2
For every value of 
The modified version of Balmer's formula is ![\frac{1}{\lambda} = R [\frac{1}{m^2} - \frac{1}{n^2} ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Clambda%7D%20%20%3D%20R%20%5B%5Cfrac%7B1%7D%7Bm%5E2%7D%20-%20%5Cfrac%7B1%7D%7Bn%5E2%7D%20%20%5D)
The Rydberg constant has a value of 
The objective of this solution is to obtain the value of n for which the wavelength of the Balmer series line is smaller than 400nm
For m = 2 and n =3
The wavelength is
![\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{3^2} ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Clambda%20%7D%20%3D%20%281.097%20%2A%2010%5E7%29%5B%5Cfrac%7B1%7D%7B2%5E2%7D%20-%20%5Cfrac%7B1%7D%7B3%5E2%7D%20%20%5D)


For m = 2 and n = 4
The wavelength is
![\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{4^2} ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Clambda%20%7D%20%3D%20%281.097%20%2A%2010%5E7%29%5B%5Cfrac%7B1%7D%7B2%5E2%7D%20-%20%5Cfrac%7B1%7D%7B4%5E2%7D%20%20%5D)


For m = 2 and n = 5
The wavelength is
![\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{5^2} ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Clambda%20%7D%20%3D%20%281.097%20%2A%2010%5E7%29%5B%5Cfrac%7B1%7D%7B2%5E2%7D%20-%20%5Cfrac%7B1%7D%7B5%5E2%7D%20%20%5D)


For m = 2 and n = 6
The wavelength is
![\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{6^2} ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Clambda%20%7D%20%3D%20%281.097%20%2A%2010%5E7%29%5B%5Cfrac%7B1%7D%7B2%5E2%7D%20-%20%5Cfrac%7B1%7D%7B6%5E2%7D%20%20%5D)


For m = 2 and n = 7
The wavelength is
![\frac{1}{\lambda } = (1.097 * 10^7)[\frac{1}{2^2} - \frac{1}{7^2} ]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Clambda%20%7D%20%3D%20%281.097%20%2A%2010%5E7%29%5B%5Cfrac%7B1%7D%7B2%5E2%7D%20-%20%5Cfrac%7B1%7D%7B7%5E2%7D%20%20%5D)


So the value of n is 7
Answer:
2.45s
Explanation:
is explanation needed too?
Answer:
Orbital Time Period is 24 years
Explanation:
This can be explained by the definition of time period.
Time period can be defined as the time taken by an object to complete one cycle, here, time taken to complete one revolution.
Also, we know that an extra solar planet which is also called as an exo planet is that planet which is outside our solar system and orbits any star other than our sun. The system in consideration is extra solar system with a single planet.
Therefore, the time taken by the parent star to move about its mass center is the orbital time period that is 24 years.
At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:

while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:

And the total energy of the system is

Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:

while the mass is moving at speed v, and therefore the kinetic energy is

And the total energy is

For the law of conservation of energy, the total energy must be conserved, therefore

. So we can write

that we can solve to find an expression for v: