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Question 958: [Quantum Physics > Line Spectra]

(a) Explain how line emission spectrum leads to an understanding of the existence of discrete electron energy levels in atoms.

(b) Some of the lines of the emission spectrum of atomic hydrogen are shown in Fig.1.

The photon energies associated with some of these lines are shown in Fig.2.

Wavelength / nm         Photon energy / 10^-19J

            410                              4.85

            434                              4.58

            486                              …

            656                              3.03

(i) Complete Fig.2 by calculating the photon energy for a wavelength of 486 nm.

(ii) Energy levels of a single electron in a hydrogen atom are shown in Fig.3.

Use data from (i) to show, on Fig.3, the transitions associated with each of the four spectral lines shown in Fig.1. Show each transition with an arrow.

Reference: Past Exam Paper – November 2009 Paper 42 Q7

Solution 958:

(a) Each line corresponds to a (specific) photon energy. A photon is emitted when an electron changes its energy level. Since the energy changes are discrete, the energy levels are also discrete.

(b)

(i) E = hc / λ = [(6.63×10^-34) × (3.0×10⁸)] / (486×10^-9) = 4.09×10^-19J

(ii) 4 transitions to / from -5.45×10^-19J level. All the transitions shown from higher to lower energy (level)

{From the magnitudes of the photon energies, it can be concluded that all the transitions would be towards the -5.45×10^-19J level. (The photon energies correspond to the difference in energy between 2 energy levels.) Since there are only 4 energy levels above the -5.45×10^-19J level, there will be a transition from each of them towards the -5.45×10^-19J level.

For example, consider photon energy of 4.85×10^-19J (for wavelength of 410nm):

Difference between energy levels: -0.60 – (-5.45) = 4.85 }

Question 959: [Kinematics > Air resistance]

A tennis ball is released from rest at top of a tall building.

Which graph best represents the variation with time t of the acceleration a of the ball as it falls, assuming that the effects of air resistance are appreciable?

Reference: Past Exam Paper – June 2004 Paper 1 Q8

Solution 959:

Answer: D.

As the ball is released from rest, its weight causes a downward acceleration on it.

Since the effects of air resistance are appreciable, as the ball falls, there is an upward resistive force due to air resistance on the ball. Thus, the resultant downward acceleration of the ball decreases with time.

Now, air resistance is not a constant force – it increases with speed. So, as the speed of the ball increases (due to its resultant downward acceleration), the effects of air resistance increases. On the graph, this is indicated by the non-linear decrease of the line.

The resultant acceleration on the ball would decrease until it becomes zero at some point – terminal speed has been reached.

Question 960: [Matter > Hooke’s law]

A trolley is held at rest between two steel springs.

Each spring has an unstretched length of 0.10 m.

Spring P has spring constant 60 N m^–1.

Spring Q has spring constant 120 N m^–1.

Spring P has an extension of 0.40 m.

What is the extension of spring Q?

A 0.10 m                     B 0.20 m                     C 0.30 m                     D 0.80 m

Reference: Past Exam Paper – November 2012 Paper 13 Q24

Solution 960:

Answer: B.

Since the trolley is held at rest, the resultant force on it is zero. That is, the tensions in both spring P and Q are equal.

Hooke’s law: F = kx

For spring P: spring constant, k = 60Nm^-1 and extension, x = 0.40m

Tension in spring P = kx = 60 × 0.40 = 24N

Now, this tension should be equal to the tension in Q.

For spring Q: tension, F = 24N and spring constant, k = 120Nm^-1

Extension x = F / k = 24 / 120 = 0.20m

Question 961: [Matter > States of Matter]

When water in a pond freezes, it changes from a liquid to a solid. When this occurs, it changes volume and exchanges energy with the surroundings.

Which row is correct?

change of volume        energy exchange

A         contracts                      gives out energy to the surroundings

B         contracts                      takes in energy from the surroundings

C         expands                       gives out energy to the surroundings

D         expands                       takes in energy from the surroundings

Reference: Past Exam Paper – June 2014 Paper 13 Q19

Solution 961:

Answer: C.

Water expands (water is a special case) when it freezes and becomes ice. Thus, its volume increases. [A and B are incorrect]

As the new bonds are formed, it gives out energy to the surroundings.

Question 962: [Atomic Physics]

Calcium nuclide ⁴²₂₀Ca is formed by beta decay.

What are the nucleon (mass) number and proton (atomic) number of the unstable nuclide that underwent beta decay to form the calcium nuclide?

nucleon number           proton number

A                     41                                19

B                     41                                21

C                     42                                19

D                     42                                21

Reference: Past Exam Paper – June 2009 Paper 1 Q39

Solution 962:

Answer: C.

Let the unstable element be ^A_ZX.

^A_ZX                  - - - >               ⁴²₂₀Ca               +                      ⁰_-1β

A = 42 + 0 = 42

Z = 20 + (-1) = 19