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Typical microwave ovens use such radiation with a wavelength of 12.2 cm. There i

ID: 889341 • Letter: T

Question


Typical microwave ovens use such radiation with a wavelength of 12.2 cm. There is an electronic transition in the H atom that could conceivably (or theoretically) produce microwave radiation of wavelength Estimate the n values between which the transition occurs. Questions to consider in completing this problem: What relationship(s) will you use to connect the wavelength to the n values? Do you expect the n values lo be relatively big or small? Why? In choosing a relationship between the unknown ns, do you expect the change in n to be the biggest or the smallest? Why? Given your expected magnitudes of the n values, what approximations can you make to avoid solving a higher degree equation for those n values?

Explanation / Answer

i) The Rydberg formula can use to connect the wavelength to n values

The formula is 1/ = R(1/n2 - 1/n1)

where is the wavelength,

R is the Rydberg constant of 1.097 * 10^7 m^-1

and the two n's are the principle quantum numbers of the states in the transition.

ii) & iii) We are looking for a transition in the 12.2 cm or 0.122 m wavelength region

    If substituted this value in above equation we will get

     (1/n2 - 1/n1) = 1/R = 1/(1.097 * 10^7 m^-1)x 0.122 m = 7.47 * 10^-7

    As n2 and n1 are separated by only one digit, n values will be relatively small

iv) By drawing up a table in a spreadsheet, to get the values of n