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Chapter 6: Q62P (page 1405)

Electrons in the lower of two spin states in a magnetic field can absorb a photon of the right frequency and move to the higher state. (a) Find the magnetic field magnitude Brequired for this transition in a hydrogen atom with n= 1 and l= 0 to be induced by microwaves with wavelength位. (b) Calculate the value of Bfor a wavelength of 4.20 cm.

Short Answer

Expert verified
  1. The magnetic field magnitude for the given transition is B=2蟺尘肠位别.
  2. The value of Bfor a wavelength of 4.20 cm is 0.255 T

Step by step solution

01

 (a) Determination of the magnetic field magnitude for the given transition.

The potential energy is given as,

U=鈥�渭zB ...(i)

Where, B is the effective magnetic field and is given as,

渭z=-2.00232e2mSz

Here, Sz=h

Thus, the energy difference is given as,

鈭�E=2.00232e2mB鈭�Sz鈮�ehmB=hc位

Solving for the magnetic field B is,

鈬�B=2蟺尘肠位别

02

 (a) Determination of the magnetic value of B for a wavelength of 4.20 cm.

From the expression for the magnetic field obtained in part (a),

B=2蟺9.11脳10-31kg3.00脳108m/s0.0420m1.60脳10-19C=0.255T

Thus the magnitude of magnetic field is 0.255 T

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