Orbitals - dynamic modules

Quantum numbers are interrelated values that indicate a specific orbital—the principal quantum number, n; the angular momentum quantum number, l; and the magnetic quantum number, ml. Which orbital is indicated by the quantum numbers n = 2, l = 1, ml = 0?

2p

Quantum numbers are interrelated values that indicate a specific orbital—the principal quantum number, n; the angular momentum quantum number, l; and the magnetic quantum number, ml. Which one of the following is an allowed set of quantum numbers?

n = 1, l = 0, ml = 0

Which transition emits the shortest wavelength of light?

n = 5 to n = 1

Atomic orbitals represent the wave functions that correspond to the solutions to the Schrödinger equation. The orbitals, which do not have specific borders or barriers, represent a volume in space where there is a high probability of finding an electron. The quantum numbers function like an address to give the location of an electron in one of the orbitals. Together, the shapes of the orbitals represent the shape of the atom. How many s orbitals exist in one energy level of an atom?

1

Quantum numbers are interrelated values that indicate a specific orbital—the principal quantum number, n; the angular momentum quantum number, l; and the magnetic quantum number, ml. What are the allowed values for the principal quantum number n?

1,2,3,..... The permitted values for the principal quantum number, n, are 1, 2, 3,... or any integer value starting with 1. The permitted values of the quantum numbers are n = 1, 2, 3.... l = 0, 1, 2,..., n−1 ml = −l,...,0,...,+l

The Rydberg equation applies to the hydrogen atom and shows the energy of light emitted or absorbed. Light is absorbed when electrons are promoted from a lower energy level to a higher energy level. Light is emitted when electrons relax from a higher energy level back down to a lower energy level. What is the wavelength of light absorbed when an electron is promoted from the n = 1 level to the n = 2 level?

121 nm ΔE = 2.18 *10 ^-18 J (1 /n^2 ^2 - 1/n^1^2 ) ΔE = 2.18 *10 ^-18 J (1 /1^2 - 1/2^2 ) ΔE = 2.18 *10 ^-18 J (1 - 0.25 ) ΔE = 1.64*10^-18 E+=hc/λ 1.64*10^-18 = (6.626*10^-34) (3.00*10^8) / λ λ= (6.626*10^-34) (3.00*10^8) /1.64*10^-18 J λ= 1.21*10^-7m 1.21*10^-7m (1nm/1*10^-9) = 121 nm <= answer

The Rydberg equation applies to the hydrogen atom and shows the energy of light emitted or absorbed. Light is absorbed when electrons are promoted from a lower energy level to a higher energy level. Light is emitted when electrons relax from a higher energy level back down to a lower energy level. Light with a wavelength of 1282 nm is emitted by an electron, which relaxes to the n = 3 level. In which level did it start?

1282nm / 10^-9 --> 1.282 *10^12 E= (6.626*10^-34) (3.00*10^8) / 1.282 *10^12 E= 1.55 *10^-37

Atomic orbitals represent the wave functions that correspond to the solutions to the Schrödinger equation. The orbitals, which do not have specific borders or barriers, represent a volume in space where there is a high probability of finding an electron. The quantum numbers function like an address to give the location of an electron in one of the orbitals. Together, the shapes of the orbitals represent the shape of the atom. Which choice ranks the given orbitals in order of increasing size?

1s < 2s < 3s

Atomic orbitals represent the wave functions that correspond to the solutions to the Schrödinger equation. The orbitals, which do not have specific borders or barriers, represent a volume in space where there is a high probability of finding an electron. The quantum numbers function like an address to give the location of an electron in one of the orbitals. Together, the shapes of the orbitals represent the shape of the atom. Which choice ranks the given orbitals in order of increasing size?

2p<3p<4p

Quantum numbers are interrelated values that indicate a specific orbital—the principal quantum number, n; the angular momentum quantum number, l; and the magnetic quantum number, ml. How many orbitals can have quantum numbers of n = 2 and l = 1?

3

Atomic orbitals represent the wave functions that correspond to the solutions to the Schrödinger equation. The orbitals, which do not have specific borders or barriers, represent a volume in space where there is a high probability of finding an electron. The quantum numbers function like an address to give the location of an electron in one of the orbitals. Together, the shapes of the orbitals represent the shape of the atom. How many p orbitals exist in one energy level (n ≥ 2) of an atom?

3 There are 3 p orbitals in each energy level. The value of the quantum number l gives the orbital shape and the possible values of ml determines the number of degenerate orbitals with that shape in each energy level. For a p orbital, l = 1 and the possible values of ml are −1, 0, and 1, so there are three p orbitals in each energy level (n ≥ 2).

Quantum numbers are interrelated values that indicate a specific orbital—the principal quantum number, n; the angular momentum quantum number, l; and the magnetic quantum number, ml. Which orbital is indicated by the quantum numbers n = 3, l = 2, ml = −1?

3d

The Rydberg equation applies to the hydrogen atom and shows the energy of light emitted or absorbed. Light is absorbed when electrons are promoted from a lower energy level to a higher energy level. Light is emitted when electrons relax from a higher energy level back down to a lower energy level. What is the wavelength of light emitted when an electron relaxes from the n = 5 level to the n = 2 level?

434 nm ΔE = 2.18 *10 ^-18 J (1 /n^2 ^2 - 1/n^1^2 ) ΔE = 2.18 *10 ^-18 J (1 /5^2 - 1/2^2 ) ΔE = 2.18 *10 ^-18 J (0.04 - 0.25 ) ΔE = -4.58*10^-19 J E= hc/λ -4.58*10^-19 J = (6.626*10^-34) (3.00*10^8) / λ λ= (6.626*10^-34) (3.00*10^8) /-4.58*10^-19 J λ= 4.34 * 10^-7 m 4.34 * 10^-7 m (1nm/1*10^-9) = 434 nm <= answer

Light with a wavelength of 1282 nm is emitted by an electron, which relaxes to the n = 3 level. In which level did it start?

5

Atomic orbitals represent the wave functions that correspond to the solutions to the Schrödinger equation. The orbitals, which do not have specific borders or barriers, represent a volume in space where there is a high probability of finding an electron. The quantum numbers function like an address to give the location of an electron in one of the orbitals. Together, the shapes of the orbitals represent the shape of the atom. How many f orbitals exist in one energy level (n ≥ 4) of an atom?

7 There are 7 f orbitals in each energy level. The value of the quantum number l gives the orbital shape, and the possible values of ml determines the number of degenerate orbitals with that shape in each energy level. For an f orbital, l = 3 and the possible values of ml are −3, −2, −1, 0, 1, 2, and 3, so there are seven f orbitals in each energy level (n ≥ 4).

Atomic orbitals represent the wave functions that correspond to the solutions to the Schrödinger equation. The orbitals, which do not have specific borders or barriers, represent a volume in space where there is a high probability of finding an electron. The quantum numbers function like an address to give the location of an electron in one of the orbitals. Together, the shapes of the orbitals represent the shape of the atom. What type of orbital is pictured here?

P

Quantum numbers are interrelated values that indicate a specific orbital - the principal quantum number, n; the angular momentum quantum number, l; and the magnetic quantum number, ml. Which one of the following is an allowed set of quantum numbers? a) n = 3, l = 1, ml = -2 b) n = 2, l = 0, ml = 1 c) n = 2, l = 2, ml = - 1 d) n = 3, l = 2, ml = - 1

The allowed set of quantum numbers is n = 3, l = 2, ml = −1 which meets all the rules for acceptable values of quantum numbers. The permitted values of the quantum numbers are n = 1, 2, 3.... l = 0, 1, 2,..., n−1 ml = −l,...,0,...,+l n = 2, l = 2, ml = −1 is not allowed because the maximum value of l is n−1. n = 3, l = 1, ml = −2 is not allowed because the values of ml must be between -l and +l. n = 2, l = 0, ml = 1 is not allowed because the values of ml must be between -l and +l.

Quantum numbers are interrelated values that indicate a specific orbital—the principal quantum number, n; the angular momentum quantum number, l; and the magnetic quantum number, ml. Which one of the following is a disallowed set of quantum numbers? a) n = 3, l = 2, ml = −2 b) n = 1, l = 0, ml = 0 c) n = 2, l = 0, ml = −1 d) n = 2, l = 1, ml = 0

The disallowed set of quantum numbers is n = 2, l = 0, ml = −1, which does not meet all the rules for acceptable values of quantum numbers because for l = 0, ml can only equal 0. The permitted values of the quantum numbers are n = 1, 2, 3.... l = 0, 1, 2,..., n−1 ml = −l,...,0,...,+l n = 2, l = 1, ml = 0; n = 1, l = 0, ml = 0; and n = 3, l = 2, ml = −2 are all allowed sets of quantum numbers.

In the Bohr model of the atom, electrons orbit the nucleus at specific energy levels. Orbits closer to the nucleus are lower in energy than those that are farther from the nucleus. a) n= 5 to n=4 b) n= 3 to n=2 c) n= 2 to n=1 d) n= 4 to n=3

c) n= 2 to n=1