The radial portion of the de Broglie wavefunction for an electron in the ground state of the hydrogen atom is $\Psi$1s(r)= 1/( $\pi a _ { 0 } ^ { 3 }$ )1/2 exp(-r/a0)where a0 is the Bohr radius.The probability of finding the electron is

A) $\left( \pi / a _ { 0 } ^ { 3 } \right) \int \exp \left( - 2 r / a _ { 0 } \right) 4 \pi r ^ { 2 } d r$. B) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) 4 \pi r ^ { 2 } d r$ C) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) d r$ D) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) d r$. E) $\frac { d } { d r } \left[ \frac { 2 } { \pi a _ { 0 } ^ { 3 } } \exp \left( - 2 r / a _ { 0 } \right) \right] \left[ \frac { 1 } { \pi a _ { 0 } ^ { 3 } } \right] ^ { 1 / 2 } e ^ { - r / a ^ { 0 } 1 / 2 }$ A) $\left( \pi / a _ { 0 } ^ { 3 } \right) \int \exp \left( - 2 r / a _ { 0 } \right) 4 \pi r ^ { 2 } d r$. B) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) 4 \pi r ^ { 2 } d r$ C) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) d r$ D) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) d r$. E) $\frac { d } { d r } \left[ \frac { 2 } { \pi a _ { 0 } ^ { 3 } } \exp \left( - 2 r / a _ { 0 } \right) \right] \left[ \frac { 1 } { \pi a _ { 0 } ^ { 3 } } \right] ^ { 1 / 2 } e ^ { - r / a ^ { 0 } 1 / 2 }$

Exam 29: Atomic Physics

Explore all topics

In an atom that has an electron in a sub-shell for which $\ell$ = 4,with respect to the magnetic field vector $\vec { B }$ the magnetic moment vector $\vec { \mu }$ of the electron is allowed to be oriented in

(Multiple Choice)

4.7/5

(83)

Question 21

What angle does the orbital angular momentum make with the z axis of a hydrogen atom in the state n = 3, $\ell$ = 2, $m _ { t }$ = -1?

(Multiple Choice)

4.7/5

(67)

Question 22

In the subshell of the Li²⁺ ion with orbital quantum number $\ell$ ,the allowed values of the magnetic quantum number $m _ { t }$ are

(Multiple Choice)

5.0/5

(72)

Question 23

In 1921,Stern and Gerlach performed an experiment that first demonstrated

(Multiple Choice)

4.8/5

(71)

Question 24

All quantum states forming a sub-shell have the same

(Multiple Choice)

4.8/5

(83)

Question 25

Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = $\ell\hbar$ .Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector $\vec { B }$ is $\sqrt { \ell ( \ell + 1 ) } \hbar$ .Which one,if either,is correct,and why?

(Multiple Choice)

4.9/5

(79)

Question 26

When electrons fill a subshell in which the orbitals have equal energy,the order in which the orbitals are filled is such that

(Multiple Choice)

4.9/5

(85)

Question 27

The radial portion of the de Broglie wavefunction for an electron in the ground state of the hydrogen atom is $\Psi$ ₁_s(r)= 1/( $\pi a _ { 0 } ^ { 3 }$ )^1/2 exp(-r/a₀)where a₀ is the Bohr radius.The probability of finding the electron is

(Multiple Choice)

4.9/5

(76)

Question 28

In a completely filled atomic shell,

(Multiple Choice)

4.7/5

(70)

Question 29

Quantum physics agrees with the classical physics limit when

(Multiple Choice)

5.0/5

(78)

Question 30

A hydrogen atom is in its first excited state (n = 2).The linear momentum of the electron is (in kg .m/s)

(Multiple Choice)

4.7/5

(87)

Question 31

Which of the following statements is true?

(Multiple Choice)

4.9/5

(82)

Question 32

One of the main problems with the Bohr model of the hydrogen atom when compared with the results of the methods of quantum mechanics used to describe atoms,was that the Bohr model predicted

(Multiple Choice)

5.0/5

(74)

Question 33

In terms of a₀,where a₀ = 0.0529 nm,the radii of the allowed orbits in the Bohr model of the hydrogen atom are given by r_n =

(Multiple Choice)

4.9/5

(75)

Question 34

The probability density of a particle at a distance r from the nucleus is essentially the

(Multiple Choice)

4.9/5

(75)

Question 35

Showing 21 - 35 of 35

Exam 29: Atomic Physics

In an atom that has an electron in a sub-shell for which ℓ\ellℓ = 4,with respect to the magnetic field vector B⃗\vec { B }B the magnetic moment vector μ⃗\vec { \mu }μ​ of the electron is allowed to be oriented in

What angle does the orbital angular momentum make with the z axis of a hydrogen atom in the state n = 3, ℓ\ellℓ = 2, mtm _ { t }mt​ = -1?

In the subshell of the Li2+ ion with orbital quantum number ℓ\ellℓ ,the allowed values of the magnetic quantum number mtm _ { t }mt​ are

In 1921,Stern and Gerlach performed an experiment that first demonstrated

All quantum states forming a sub-shell have the same

When electrons fill a subshell in which the orbitals have equal energy,the order in which the orbitals are filled is such that

The radial portion of the de Broglie wavefunction for an electron in the ground state of the hydrogen atom is Ψ\PsiΨ 1s(r)= 1/( πa03\pi a _ { 0 } ^ { 3 }πa03​ )1/2 exp(-r/a0)where a0 is the Bohr radius.The probability of finding the electron is

In a completely filled atomic shell,

Quantum physics agrees with the classical physics limit when

A hydrogen atom is in its first excited state (n = 2).The linear momentum of the electron is (in kg .m/s)

Which of the following statements is true?

One of the main problems with the Bohr model of the hydrogen atom when compared with the results of the methods of quantum mechanics used to describe atoms,was that the Bohr model predicted

In terms of a0,where a0 = 0.0529 nm,the radii of the allowed orbits in the Bohr model of the hydrogen atom are given by rn =

The probability density of a particle at a distance r from the nucleus is essentially the

Introduction and Vectors

Motion in One Dimension

Motion in Two Dimensions

The Laws of Motion

More Applications of Newtons Laws

Energy of a System

Conservation of Energy

Momentum and Collisions

Relativity

Rotational Motion

Gravity,planetary Orbits,and the Hydrogen Atom

Oscillatory Motion

Mechanical Waves

Superposition and Standing Waves

Fluid Mechanics

Temperature and the Kinetic Theory of Gases

Energy in Thermal Processes: the First Law of Thermodynamics

Heat Engines,entropy,and the Second Law of Thermodynamics

Electric Forces and Electric Fields

Electric Potential and Capacitance

Current and Direct Current Circuits

Magnetic Forces and Magnetic Fields

Faradays Law and Inductance

Electromagnetic Waves

Reflection and Refraction of Light

Image Formation by Mirrors and Lenses

Wave Optics

Quantum Physics

Nuclear Physics

Particle Physics

Filters

In an atom that has an electron in a sub-shell for which $\ell$ = 4,with respect to the magnetic field vector $\vec { B }$ the magnetic moment vector $\vec { \mu }$ of the electron is allowed to be oriented in

What angle does the orbital angular momentum make with the z axis of a hydrogen atom in the state n = 3, $\ell$ = 2, $m _ { t }$ = -1?

In the subshell of the Li²⁺ ion with orbital quantum number $\ell$ ,the allowed values of the magnetic quantum number $m _ { t }$ are

The radial portion of the de Broglie wavefunction for an electron in the ground state of the hydrogen atom is $\Psi$ ₁_s(r)= 1/( $\pi a _ { 0 } ^ { 3 }$ )^1/2 exp(-r/a₀)where a₀ is the Bohr radius.The probability of finding the electron is

In terms of a₀,where a₀ = 0.0529 nm,the radii of the allowed orbits in the Bohr model of the hydrogen atom are given by r_n =