A hypothetical atom has energy levels uniformly separated by 1.2 eV . At a temperature of 2000 K, what is the ratio of the number of atoms in the excited state to the number in the excited state?
The ratio of the number of atoms in the excited state to the number of atoms in the excited state is .
The energy difference between two atomic levels of an atom,
The temperature of the states,
Number of atoms in the higher-energy state,
Number of atoms in the lower-energy state,
The Boltzmann distribution is a probability function used in statistical physics to define the state of a particle system in terms of temperature and energy.
Using the Boltzmann-distribution equation which is the expression for the probability for stimulated emission of radiation to the probability for spontaneous emission of radiation under thermal equilibrium, we can get the required ratio of the number of atoms present in the excited state to that present in the excited state.
The Boltzmann energy distribution equation,
Here, Boltzmann constant,
The energy difference between any two levels is,
So, the energy difference between the 13th excited state and the 11th excited state is given as:
Now, using this energy difference value in the equation (i) with the given data, we can get the ratio of the number of atoms in the 13th excited state to the number of atoms in the 11th excited state as follows:
Hence, the value of the required ratio is .
The beam from an argon laser (of wavelength 515 nm) has a diameter 3.00 mm of and a continuous energy output rate of 5.00 W. The beam is focused onto a diffuse surface by a lens whose focal length f is 3.50 cm . A diffraction pattern such as that of Fig. 36-10 is formed, the radius of the central disk being given by (see Eq. 36-12 and Fig. 36-14). The central disk can be shown to contain 84% of the incident power. (a) What is the radius of the central disk? (b) What is the average intensity (power per unit area) in the incident beam? (c) What is the average intensity in the central disk?
Here are the wavelengths of a few elements:
Make a Moseley plot (like that in Fig. 40-16) from these data and verify that its slope agrees with the value given for C in Module 40-6.
In 1911, Ernest Rutherford modeled an atom as being a point of positive charge surrounded by a negative charge -ze uniformly distributed in a sphere of radius centered at the point. At distance within the sphere, the electric potential is .
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