energy level equation?

Question

using the formula = E^n=218.0x10^ -20/n^2 Joules

where n is the energy level
find the solution if n = 3, and again if n= 4
* Keep all number relative to 10^ -20 for graphing.

thankyou.

Answer 1

E^n=218.0*10^-20/n^2
E^3=218.0/9*10^-20
=24.2*10^-20 J
E^4=218.0/16*10^-20
=13.7^10^-20 J

Answer 2

E^n=218.0x10^ -20/n^2 Joules

Your equation is a bit confusing.
Do you mean [218 * 10^-20]/n^2 , or
do you mean 218 * 10^(-20/n^2)?

If it is the 1st case, then the answer is:
E^3 = (218/9) * 10^-20 = 24.22 * 10^-20, and
E^4 = (218/16) * 10^-20 = 13.625 *10^-20

Now it is unclear if the above is the final answer you are seeking , or do you wish to find E in each case?

If it is E you are seeking, then the answers are:
for n=3, E=(24.22)^1/3 * (10^-20)^1/3, and
for n=4, E = (13.625)^1/4 * (10^-20)^1/4

For the case n=4 this would give E= 1.92125109 * 10^-5
To keep this relative to 10^-20, move the decimal point 15 places to the right and change the 10^-5 to 10^-20. Somehow, I don't think this is what you were looking for.

Answer 3

If I understood what you wanted:
E^n = 218.0 x 10^ (-20)/n^2
= 218.0/n^2 x 10^ (-20)

For n = 3
E^3 = 218.0/3^2 x 10^ (-20)
= 24.22 x 10^ (-20)

For n = 4
E^4 = 218.0/4^2 x 10^ (-20)
= 13.63 x 10^ (-20)

Answer 4

Do you want to solve for E? or E^n?

Is the n^2 on the right in the exponent? If so, I get:

n------------E
3------------1.03
4------------1.17

If it's in the denominator, I get:

n --------E----------------E^n
3-------6.23E-7 ------24.22E-20
4-------1.92E-5------13.66E-20