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When electrons bombard a molybdenum target, they produce both continuous and characteristic x-rays as shown in Fig. 40-13. In that figure the kinetic energy of the incident electrons is 35.0 keV. If the accelerating potential is increased to 50.0 keV, (a) what is the value of min, and (b) do the wavelengths of the role="math" localid="1661497027757" kand klines increase, decrease, or remain the same?

Short Answer

Expert verified
  1. The value of the minimum wavelength is 24.8 pm .
  2. The wavelengths of the linesk and kremain same.

Step by step solution

01

The given data:

  1. The striking of electrons on the molybdenum target produces continuous and characteristic x-rays.
  2. The kinetic energy of the incident electrons is 35 keV .
  3. Increased energy due to accelerating potential, E=50keV
02

Understanding the concept of wavelength due to accelerating potential:

Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the magnetic frequency of the photon and thus, equally, equates to the wavelength of the wave. When the frequency of photons is high, its potential is high.

Formulas:

The kinetic energy gained by the electron is,

E=eV 鈥.. (1)

Here, e is the charge and V is the accelerating potential difference.

The energy of the photon due to Planck鈥檚 relation is,

E=hc 鈥.. (2)

Here, is the Plank鈥檚 constant, c is the speed of light, and is the wavelength.

03

 Step 3: (a) Calculation of the minimum wavelength:

Equating both the equations (1) and (2), the value of the minimum wavelength using the data is as follow.

eV=hcminmin=hceVeV=hcminmin=6.6310-34J.s3108m/s50103keV1.610-19J/eV=24.810-12m=24.8pm

Hence, the value of the wavelength is 24.8 pm.

04

(b) Calculation of the wavelengths of Kα and Kβ lines:

The values of wavelengths of the lines Kand Kdo not depend on the external potential.

Hence, the wavelengths of the lines remain the same irrespective of the accelerating potential.

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Most popular questions from this chapter

Martian CO2laser. Where sunlight shines on the atmosphere of Mars, carbon dioxide molecules at an altitude of about 75 km undergo natural laser action. The energy levels involved in the action are shown in Fig. 40-26; population inversion occurs between energy levels E1and E2. (a) What wavelength of sunlight excites the molecules in the lasing action? (b) At what wavelength does lasing occur? (c) In what region of the electromagnetic spectrum do the excitation and lasing wavelengths lie?

A 20 keV electron is brought to rest by colliding twice with target nuclei as in Fig. 40-14. (Assume the nuclei remain stationary.) The wavelength associated with the photon emitted in the second collision is 130 pm greater than that associated with the photon emitted in the first collision. (a) What is the kinetic energy of the electron after the first collision? What are (b) the wavelength 1and (c) the energy E1associated with the first photon? What are (d) 2and (e) E2associated with the second photon?

A hypothetical atom has only two atomic energy levels, separated by 32 eV . Suppose that at a certain altitude in the atmosphere of a star there are 6.11013/cm3of these atoms in the higher-energy state and 2.51015/cm3in the lower-energy state. What is the temperature of the star鈥檚 atmosphere at that altitude?

Figure 40-24 shows the energy levels of two types of atoms. Atoms A are in one tube, and atoms B are in another tube. The energies (relative to ground-state energy of zero) are indicated; the average lifetime of atoms in each level is also indicated. All the atoms are initially pumped to levels higher than the levels shown in the figure. The atoms then drop down through the levels, and many become 鈥渟tuck鈥 on certain levels, leading to population inversion and lasing. The light emitted by A illuminates B and can cause stimulated emission of B. What is the energy per photon of that stimulated emission of B?

Here are theK wavelengths of a few elements:

Element

位(辫尘)

Element

位(辫尘)

Ti

275

Co

179

V

250

Ni

166

Cr

229

Cu

154

Mn

210

Zn

143

Fe

193

Ga

134

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.

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