1.5: Unit 1 Practice Problems
Unit 1A
Exercise 1
What is true about the Rutherford atom model?
- It explains why atoms do not send out electromagnetic radiation permanently
- It explains why alpha particles get scattered by atoms
- It explains the atomic spectrum of the hydrogen atom
- It explains the wave-particle dualism
- Answer
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b) It explains why alpha particles get scattered by atoms
Exercise 2
The Bohr radius (the radius of the electron orbit for the H atom in its ground state) is 5.29 x 10 -11 m. Calculate the radius of an electron in the third shell of the H atom according to the Bohr atom model.
- Answer
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r 3 = 3 2 x 5.29 x 10 -11 m = 47.61 x 10 -11 m.
Exercise 3
The electron in an H atom undergoes an electronic transition from the 3 rd to the 2 nd shell. What frequency does the light that is emitted have? The energy of the electron in the first shell is -2.18 x 10 -18 J.
- Answer
-
Energy of electron in the 3 rd shell: E 3 = -2.18 x 10 -18 J / 3 2 = -0.24 x 10 -18 J
Energy of electron in the 2 nd shell: E 2 = -2.18 x 10 -18 J / 2 2 = -0.545 x 10 -18 J
Energy difference between the two electrons: E 3 -E 2 = 0.305 x 10 -18 J
Frequency of emitted light: n=(E 3 -E 2 )/h = 0.305 x 10 -18 J/ 6.63 x 10 -34 Js = 4.60 x 10 14 s -
Exercise 4
What is the mass of a photon with a wavelength of 400 nm that travels though space?
- Answer
-
λ = h/mc --> m = h/λc = 6.63 x 10 - 34 Js / (400 x 10 -9 m x 3.00 x 10 8 m/s) = 5.525 x 10 -36 kg.
Exercise 5
Two objects are moving at the same speed. Which (if any) of the following statements are true?
- The DeBroglie wavelength of the heavier object is longer than that of the lighter one.
- If one object has twice as much mass as the other, its wavelength is one-half of the other
- Doubling the speed of one of the objects will have the same effect on its wavelength as doubling its mass.
- Answer
-
a) If one object has twice as much mass as the other, its wavelength is one-half of the other
b) Doubling the speed of one of the objects will have the same effect on its wavelength as doubling its mass
Exercise 6
The power of a red laser with a wavelength of 630 nm) is 1.00 Watt (1.00 Js). How many photons per second does the laser emit?
- Answer
-
Unit 1B
Exercise 7
Which of the following waves would you consider to be standing matter wave?
- The vibration of a drum.
- Sound traveling through open air.
- A tsunami.
- None of the above.
- Answer
-
a) The vibration of a drum.
Exercise 8
What are orbitals (more than one answer can be correct)?
- Wave functions that describe the electrons as three-dimensional standing matter waves in an atom.
- Spaces inside an atom in which the electron travels as a classical particle.
- Solutions of the Schrödinger equation for the hydrogen atom.
- Answer
-
a) Wave functions that describe the electrons as three-dimensional standing matter waves in an atom.
c) Solutions of the Schrödinger equation for the hydrogen atom.
Exercise 9
Which quantum numbers l are allowed when the quantum number n is 4?
- Answer
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l can be 3,2,1,0
Exercise 10
Which quantum numbers m are allowed when the quantum number l is 3?
- Answer
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-3,-2,-1,0,+1,+2,+3
Exercise 11
What is true about the following wave function?
\[\Psi=\frac{1}{\sqrt{2 \pi}} \quad \frac{\sqrt{6}}{2} \cos \theta \quad \frac{4}{81 \sqrt{6} a_0 3 / 2}\left[6-\frac{r}{a_0}\right] \frac{r}{a_0} e^{-r / 3 a_0} \nonumber\]
- Its does not have angular nodes
- Its does not have spherical nodes
- Its amplitude is 0 at the nucleus
- The wave function represents an s orbital
- Answer
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c) Its amplitude is 0 at the nucleus
Exercise 12
The angular part of the wavefunction of an orbital has the following form:
\[\Theta \Phi(x, y, z)=\frac{1}{4} \sqrt{\frac{15}{\pi}} \frac{\left(x^2-y^2\right)}{r^2} \nonumber\]
Which planes are the planar nodes in this orbital?
- Answer
-
The wavefunction is 0 for x=y and x=-y. So it is two planes that bisect the x and the y axis.
Unit 1C
Exercise 13
Order the following orbitals with respect to their penetration abilities:
4s, 4p, 4d, 4f
- Answer
-
4s > 4p > 4d > 4f
Exercise 14
What is the effective nuclear charge on an electron in an He + ion?
- Answer
-
Exercise 15
Calculate the orbital energy of a 3p electron in a sulfur atom using the Slater rules.
- Answer
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(1s 2 ) (2s 2 2p 6 ) (3s 2 3p 4 )
Exercise 16
Calculate the orbital energy of a 3d electron in a palladium atom using the Slater rules.
- Answer
-
(1s 2 ) (2s 2 2p 6 ) (3s 2 3p 6 )(3d 10 )(4s 2 4p 6 )(4d 8 )(5s 2 )
Exercise 17
Calculate how much higher the first ionization energy of an oxygen atom is compared to a fluorine atom. Use the Slater rules to answer the question.
- Answer
-
O: (1s 2 ) (2s 2 2p 4 )
Dr. Kai Landskron ( Lehigh University ). If you like this textbook, please consider to make a donation to support the author's research at Lehigh University: Click Here to Donate .