HSC Exam-Style Question Practice Week 1 PDF

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Past hard HSC questions and my response to them...

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HSC Exam-Style Question Practice Set 1 Question 1 (4 marks) A dart player releases a dart 2.4 m away from the dartboard where the bullseye is 1.7 m from the ground. The player successfully hits the bullseye by throwing from a height of 1.5 m at an angle of 30° above the horizontal.

Determine the initial velocity of the dart.

Question 2 (4 marks) A bar magnet is placed on a sensitive electronic balance as shown in the diagram. A hollow solenoid is held stationary, such that the magnet is partly within the solenoid.

The solenoid is then lifted straight up without touching the magnet. (a) Explain the changes that you would expect to observe on the electronic balance. (2 marks) When the solenoid is slowly lifted, the solenoid will experience a change in flux and according to Faraday’s Law(Formula) will induce an emf in the solenoid. This EMF will attempt to induce a current due to Lenz’s Law however, since the circuit is open between X and Y, no current will flow and hence, there is no opposing current. As a result, the bar magnet will not experience an opposing force and there will be no observable change on the electronic balance. (b) A voltmeter and an ammeter were then connected in series between points X and Y and the experiment was repeated. Explain what would be observed on the two meters. (4 marks) When the solenoid is slowly lifted, the solenoid will experience a change in flux and according to Faraday’s Law(Formula) induces an emf in the solenoid. A voltmeter and ammeter will complete the circuit between X and Y which means a current can flow due to Lenz’s law and this current will flow in such a direction to give rise to an opposing magnetic field to the initial change. Reading: Even though the voltmeter is connected in series, there is an observable value on the voltmeter due to the solenoid experiencing a change in flux that induces an emf according to Faraday’s Law. But the voltmeter has a high resistance due to V = IR and I decreases to 0 on the ammeter since the incorrectly set up voltmeter causes the circuit to behave like an open circuit. Thus, no reading is recorded on the ammeter.

Question 3 (5/5 marks) In 1902, Lenard conducted an experiment to study photoelectrons. The results he obtained did not match those predicted by theory. Lenard’s experimental apparatus is shown below.

The results for the experiment are summarised in the table: Characteristic

Classical Predictions

Experimental results

Intensity

As the intensity of the light increases the photocurrent will increase.

Above a threshold frequency as intensity increased so did photocurrent.

Emission time

For low intensities, it should be very long.

If emission occurred, it was instantaneous.

Frequency

Emission is independent of frequency.

Emission is frequency dependent. Below threshold frequency no electrons emitted.

Energy

As light intensity increases, the kinetic energy of the photoelectrons will increase.

EK remains constant with increased intensity but varies with the type of surface and the frequency.

Albert Einstein, however, was able to explain these results with a new theory of light. Einstein was later to receive a Nobel prize for this work. Outline Einstein’s explanation of these results. Answer: The photoelectric effect explains the phenomena where a specific wavelength/frequency of light causes the emission of electrons as photocurrent. Einstein’s model: Einstein explained Leonard’s practical results with his proposal of a new model of light, as a photon which is a small packet of quantised energy E = hf. He suggested for the photoelectric effect that there exists a threshold frequency for each metal where light below that level would result in no emission. Furthermore, this contributed to the suggestion of a work function which is unique for each metal and is the required energy of a photon for emission to occur. As a result, it could be concluded that a photon interacts on a 1:1 basis with an instantaneous emission of electrons or no emission if it doesn’t have enough energy. Observation: Intensity Einstein’s model suggested that intensity was linked to the amount of photons emitted with a higher intensity of light correlating to greater photons. This also meant that the energy of the photon must be above the threshold frequency of the metal such that emission could occur and hence, if emission is greater, there would be a higher amount of photons. Since the photons would have enough energy to liberate electrons, more numerous photons means greater electrons and thus, photocurrent. Observation: Emission time Einstein postulated that since the interaction between photon and electron was on a 1:1 basis and hence, if the energy of the photon was greater than the work function emission would occur instantaneously. Likewise, if the energy of the photon was lower than the work function, there would be no emission. Observation: Frequency Einstein believed that the frequency of the light correlated with the energy of the photon so at a higher frequency, the energy of the photon would be higher. Hence, above a certain frequency, the energy of each photon is generally higher than the work function such that emission and photocurrent can occur. Therefore, below this frequency, no emission can occur because photons do not have enough energy to overcome work function. Observation: Energy Einstein proposed a formula E(k) = hf - hf0 which is derived from the conservation of energy, where the kinetic energy of the photon

is the remaining energy from the emission and thus, E - (Work function) gives the kinetic energy of the photon.Therefore, since the work function is different for various metals and the energy of the photon is dependent on the frequency of light, the KE of particles will be different.

Question 4 (6/6 marks) The success of the Bohr model of the hydrogen atom is based on its ability to address two issues: ●

the limitations of the Rutherford model, and;

●

observations of the emission spectrum of the hydrogen atom.

Assess the validity of this statement. The statement is fairly true because the Bohr model addresses limitations of the Rutherford model and includes the Balmer series(observations of emission spectrum of the hydrogen atom.) Bohr’s model: Bohr built upon the failures of Rutherford and included the use of the Balmer series which are a series of Hydrogen spectra lines that have been measured and exist in the visible spectrum. Postulates: 1. 2. 3.

Nucleus consists of protons and neutrons with electrons orbiting in stable orbits around the nucleus via electromagnetic attraction Electrons must absorb/release photons equivalent to the energy required to move between states(Instantaneous transitions) Electron orbits have quantised angular momentum which follows

L=mvr=

nh 2π

Bohr accounted for some of the limitations of Rutherford’s model Limitation 1: Electrons which orbit the nucleus in circular orbits are accelerating and thus, according to Ampere’s Law should emit EMR. This EMR must come from the KE of the electrons by the Law of CoE and hence, the electron must eventually collide with the nucleus. So how is the orbit stable? Bohr’s solution: He postulated that electrons have stable orbits around the nucleus but could not fully explain how until De Broglie and Schrodinger helped solve it Limitation 2: Rutherford could not account for the spectral lines of emission, absorption and continuous spectra Bohr’s solution: Building upon the Balmer series, which is a set of visible Hydrogen spectral lines. Bohr factored this by suggesting that electrons moving between orbits emit EMR(second postulate) which shows up as the spectral lines. Limitation 3: Rutherford failed to fully explain the components of the nucleus Solution: Bohr built upon the discovery of the neutron and proton, he postulated that both of them existed in the nucleus together at very small distances

f ¿2 ¿ 2 i¿ n(¿) n¿ 1 ¿

which is used to calculate the wavelengths of the emission lines

1 =R ¿ ƛ However, he still failed to explain other phenomena and limitations including: -

If the nucleus is made up of dense protons and neutrons, how is it held together because the electrostatic repulsion should repel particles He still could not account for the stability of orbits(De Broylie helped solve this problem later on) The Balmer series is only true for hydrogen Close observation of spectral lines reveals many fine spectral lines(stark effect) When a magnetic field is applied to atoms, spectral lines are spread out across the spectrum(Zeeman effect)

Therefore, the statement is invalid because it successfully accounts for some failures such as Spectral lines, nucleus but it also leaves many limitations such as failing to fully explain how the electrons orbit in stable states until Schrodinger and De Broglie helped develop the model. Frew H/w: Analyse the contribution of Schrodinger to the current model of the atom(5) Faults of previous model: Bohr and Rutherford could not fully account for how electrons were able to orbit the nucleus in stable orbits Schrodinger addressed the faults of the Rutherford and Bohr’s model through the incorporation of Heisenberg’s uncertainty principle

Δ xp (x)≥

h 4π

. This principle suggested there was a fundamental limit with measuring the displacement and

velocity of an object at an exact time, Schrodinger applied this to the model of the atom through the suggestion that it was impossible to know where an electron was exactly and how fast it was travelling. Schrodinger’s model: Schrodinger introduced his quantum mechanical model of the atom which postulated that electrons orbited in probability clouds where the electron could be anywhere within the region of the nucleus however, most of the time it was within the orbits. His model also included previous postulates by De Broglie that electrons orbited in standing waves which conserved energy and could fully account for the stability of electron orbits. Conclusion: Therefore, Schrodinger’s has contributed significantly with his postulates to the current quantum mechanical model of the atom and has helped solve some limitations of previous models by proposing probability clouds....