Answer:
80% (Eighty percent)
Explanation:
The material has a refractive index (n) of 1.25
Speed of light in a vacuum (c) is 2.99792458 x 10⁸ m/s
We can find the speed of light in the material (v) using the relationship
n = c/v, similarly
v = c/n
therefore v = 2.99792458 x 10⁸ m/s ÷ (1.25) = 239 833 966 m/s
v = 239 833 966 m/s
Therefore the percentage of the speed of light in a vacuum that is the speed of light in the material can be calculated as
(v/c) × 100 = (1/n) × 100 = (1/1.25) × 100 = 0.8 × 100 = 80%
Therefore speed of light in the material (v) is eighty percent of the speed of light in the vacuum (c)
The electrical potential energy of a charge q located at a point at potential V is given by

Therefore, if the charge must move between two points at potential V1 and V2, the difference in potential energy of the charge will be

In our problem, the electron (charge e) must travel across a potential difference V. So the energy it will lose traveling from the metal to the detector will be equal to

Therefore, if we want the electron to reach the detector, the minimum energy the electron must have is exactly equal to the energy it loses moving from the metal to the detector:
Explanation:
Below is an attachment containing the solution
The frequency of the radio wave is:

The wavelength of an electromagnetic wave is related to its frequency by the relationship

where c is the speed of light and f the frequency. Plugging numbers into the equation, we find

and this is the wavelength of the radio waves in the problem.
The energy transferred to the spring is given by:

where
k is the spring constant
x is the elongation of the spring with respect its initial length
Let's convert the data into the SI units:


so now we can use these data inside the equation ,to find the energy transferred to the spring: