# earth science questions 1

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**Recall that Planck introduced ***h*** to describe the possible energies of a radiation oscillator in a cavity wall. The result was ε = ***nhf*** where ***n = ***0, 1, 2, … and ***f*** is the frequency of the oscillator. **

a) **What are the dimensions of ***h***? **

b) **It is reasonable to expect electrons in an atom are bound due to an electrostatic force ***ke***2****/***r***2***.*** Consider a Hydrogen atom. Assuming the size of the electron orbit can only depend on the electronic charge ***e***, the electron mass ***m,***and Planck’s constant ***h, ***use dimensional analysis to determine how the size of the orbit ***r*** must depend on ***e, m, ***and ***h. ***Use your result to estimate the size of an H atom. Is the size of such an orbit unambiguously determined by classical considerations? **

c) **Show that the “fine structure constant” α ≡ 2π***ke***2****/***hc*** is dimensionless and evaluate its value. **

d) **It is speculated that quantum mechanical effects are important for the gravitational interaction at a distance scale called the ***Planck length***. Using dimensional considerations determine how the Planck length depends on ***G, h,*** and ***c. ***Evaluate its value. **

2. **Assume the energy of a photon of frequency ***f ***to be given by ε = ***hf. ***Consider light produced by a 50W monochromatic Sodium light source of wavelength λ = 590nm. **

**a) ****Determine the energy of each photon in the Na light**

**b) ****At a distance of 40cm from the light source what is the density of photons per unit volume**?

**c) ****What is the rate at which photons enter an eye pupil of area ***A =*** 2mm****2**** for the location of part (b)? **

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