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37. When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the or- bital angular momentum l. This is the selection rule, which states that Al = ±1, that is, in a transition, the value of can only increase or decrease by one. Ac- cording to this rule, which of the following transitions are allowed: (a) 2s 1s, (b) 3p1s, (c) 3d 4f, (d) 4d →→→ 3s? In view of this se- lection rule, explain why it is possible to observe the various emission series shown in Figure 7.11. 38. In an electron microscope, electrons are accelerated by passing them through a voltage difference. The ki- netic energy thus acquired by the electrons is equal to the voltage times the charge on the electron. Thus, a voltage difference of 1 V imparts a kinetic energy of 1.602 x 1019 CX V or 1.602 × 10-19 J. Calculate the wavelength associated with electrons accelerated by 5.00 x 10³ V. 39. A microwave oven operating at 1.22 × 108 nm is used to heat 150 mL of water (roughly the volume of a tea cup) from 20°C to 100°C. Calculate the number of photons needed if 92.0 percent of microwave energy is converted to the thermal energy of water. 40. The radioactive Co-60 isotope is used in nuclear med- icine to treat certain types of cancer. Calculate the wavelength and frequency of an emitted gamma par- ticle having the energy of 1.29 × 10¹¹ J/mol. 41. (a) An electron in the ground state of the hydrogen atom moves at an average speed of 5 × 106 m/s. If the speed is known to an uncertainty of 1 percent, what is the uncertainty in knowing its position? Given that the radius of the hydrogen atom in the ground state is 5.29 x 10 m, comment on your result. The mass of an electron is 9.1094 × 1031 kg. (b) A 0.15-kg base- ball thrown at 100 mph has a momentum of 6.7 kg - m/s. If the uncertainty in measuring the momentum is 1.0 × 107 of the momentum, calculate the uncertainty in the baseball's position.

37. When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the or- bital angular momentum l. This is the selection rule, which states that Al = ±1, that is, in a transition, the value of can only increase or decrease by one. Ac- cording to this rule, which of the following transitions are allowed: (a) 2s 1s, (b) 3p1s, (c) 3d 4f, (d) 4d →→→ 3s? In view of this se- lection rule, explain why it is possible to observe the various emission series shown in Figure 7.11. 38. In an electron microscope, electrons are accelerated by passing them through a voltage difference. The ki- netic energy thus acquired by the electrons is equal to the voltage times the charge on the electron. Thus, a voltage difference of 1 V imparts a kinetic energy of 1.602 x 1019 CX V or 1.602 × 10-19 J. Calculate the wavelength associated with electrons accelerated by 5.00 x 10³ V. 39. A microwave oven operating at 1.22 × 108 nm is used to heat 150 mL of water (roughly the volume of a tea cup) from 20°C to 100°C. Calculate the number of photons needed if 92.0 percent of microwave energy is converted to the thermal energy of water. 40. The radioactive Co-60 isotope is used in nuclear med- icine to treat certain types of cancer. Calculate the wavelength and frequency of an emitted gamma par- ticle having the energy of 1.29 × 10¹¹ J/mol. 41. (a) An electron in the ground state of the hydrogen atom moves at an average speed of 5 × 106 m/s. If the speed is known to an uncertainty of 1 percent, what is the uncertainty in knowing its position? Given that the radius of the hydrogen atom in the ground state is 5.29 x 10 m, comment on your result. The mass of an electron is 9.1094 × 1031 kg. (b) A 0.15-kg base- ball thrown at 100 mph has a momentum of 6.7 kg - m/s. If the uncertainty in measuring the momentum is 1.0 × 107 of the momentum, calculate the uncertainty in the baseball's position.

Physical Chemistry
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom
Section: Chapter Questions
Problem 11.24E: Based on the trend shown in Figure 11.5, draw the probability distribution of a harmonic oscillator...
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37. When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the or- bital angular momentum l. This is the selection rule, which states that Al = ±1, that is, in a transition, the value of can only increase or decrease by one. Ac- cording to this rule, which of the following transitions are allowed: (a) 2s 1s, (b) 3p1s, (c) 3d 4f, (d) 4d →→→ 3s? In view of this se- lection rule, explain why it is possible to observe the various emission series shown in Figure 7.11. 38. In an electron microscope, electrons are accelerated by passing them through a voltage difference. The ki- netic energy thus acquired by the electrons is equal to the voltage times the charge on the electron. Thus, a voltage difference of 1 V imparts a kinetic energy of 1.602 x 1019 CX V or 1.602 × 10-19 J. Calculate the wavelength associated with electrons accelerated by 5.00 x 10³ V. 39. A microwave oven operating at 1.22 × 108 nm is used to heat 150 mL of water (roughly the volume of a tea cup) from 20°C to 100°C. Calculate the number of photons needed if 92.0 percent of microwave energy is converted to the thermal energy of water. 40. The radioactive Co-60 isotope is used in nuclear med- icine to treat certain types of cancer. Calculate the wavelength and frequency of an emitted gamma par- ticle having the energy of 1.29 × 10¹¹ J/mol. 41. (a) An electron in the ground state of the hydrogen atom moves at an average speed of 5 × 106 m/s. If the speed is known to an uncertainty of 1 percent, what is the uncertainty in knowing its position? Given that the radius of the hydrogen atom in the ground state is 5.29 x 10 m, comment on your result. The mass of an electron is 9.1094 × 1031 kg. (b) A 0.15-kg base- ball thrown at 100 mph has a momentum of 6.7 kg - m/s. If the uncertainty in measuring the momentum is 1.0 × 107 of the momentum, calculate the uncertainty in the baseball's position.
Transcribed Image Text:37. When an electron makes a transition between energy levels of a hydrogen atom, there are no restrictions on the initial and final values of the principal quantum number n. However, there is a quantum mechanical rule that restricts the initial and final values of the or- bital angular momentum l. This is the selection rule, which states that Al = ±1, that is, in a transition, the value of can only increase or decrease by one. Ac- cording to this rule, which of the following transitions are allowed: (a) 2s 1s, (b) 3p1s, (c) 3d 4f, (d) 4d →→→ 3s? In view of this se- lection rule, explain why it is possible to observe the various emission series shown in Figure 7.11. 38. In an electron microscope, electrons are accelerated by passing them through a voltage difference. The ki- netic energy thus acquired by the electrons is equal to the voltage times the charge on the electron. Thus, a voltage difference of 1 V imparts a kinetic energy of 1.602 x 1019 CX V or 1.602 × 10-19 J. Calculate the wavelength associated with electrons accelerated by 5.00 x 10³ V. 39. A microwave oven operating at 1.22 × 108 nm is used to heat 150 mL of water (roughly the volume of a tea cup) from 20°C to 100°C. Calculate the number of photons needed if 92.0 percent of microwave energy is converted to the thermal energy of water. 40. The radioactive Co-60 isotope is used in nuclear med- icine to treat certain types of cancer. Calculate the wavelength and frequency of an emitted gamma par- ticle having the energy of 1.29 × 10¹¹ J/mol. 41. (a) An electron in the ground state of the hydrogen atom moves at an average speed of 5 × 106 m/s. If the speed is known to an uncertainty of 1 percent, what is the uncertainty in knowing its position? Given that the radius of the hydrogen atom in the ground state is 5.29 x 10 m, comment on your result. The mass of an electron is 9.1094 × 1031 kg. (b) A 0.15-kg base- ball thrown at 100 mph has a momentum of 6.7 kg - m/s. If the uncertainty in measuring the momentum is 1.0 × 107 of the momentum, calculate the uncertainty in the baseball's position.
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