# Physics 9702 Doubts | Help Page 198

__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

^{-19}J
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 / Î» = [(6.63×10

^{-34}) × (3.0×10^{8})] / (486×10^{-9}) = 4.09×10^{-19}J
(ii) 4 transitions to / from -5.45×10

^{-19}J 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

^{-19}J 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^{-19}J level, there will be a transition from each of them towards the -5.45×10^{-19}J level.
For example, consider
photon energy of 4.85×10

^{-19}J (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

^{42}_{20}Ca 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}_{Z}X.^{A}

_{Z}X - - - >

^{42}

_{20}Ca +

^{0}

_{-1}Î²

A = 42 + 0 = 42

Z = 20 + (-1) = 19

Please consider answering ALL of the following questions:

ReplyDelete4/O/N/02 Q.5(b),Q.6(c)(i)

6/O/N/02 Q.11(a)(b)

6/O/N/03 Q.9

04/M/J/04 Q.8(a),(b)(i),(ii)1.

06/M/J/04 Q.9(b)(iii),Q.11(b)

06/O/N/04 Q.3(b)(i)1.,Q.4(a),Q.6(b),Q.8(a)(i)

04/M/J/05 Q.7(a)

06/O/N/05 Q.8(b),Q.10(a)

04/M/J/06 Q.6(a),(c),Q.7(b)

06/M/J/06 Q.14(b)

04/O/N/06 Q.3(c)

06/O/N/06 Q.3(b)

05/M/J/07 Q.2(d)

04/O/N/07 Q.7(b)(i),(c),Q.10(c)

04/M/J/08 Q.3(c)(ii),Q.5(b),Q.9(b),Q.11(a)(ii)

04/O/N/08 Q.7(c)

04/M/J/09 Q.11(b)(iii)

41/O/N/09 Q.6(a),(b)(i),Q.10

41/M/J/10 Q.6(a),Q.7(a)

51/M/J/10 Q.2(d)

41/M/J/11 Q.8(a)

For 04/M/J/08 Q.3(c)(ii), see solution 963 at

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