The scope of an experiment goes at the very beginning of it. It includes a general introduction to the topic of investigation as well as personal interest.
The research question of an experiment is a hyper-focused and specific question related to the topic. It contains and asks about the effect of an **independent variable** on a **dependent variable**.
### Background information and hypothesis
!!! note
This section can instead be placed immediately before the research question depending on the experiment.
In this section, scientific theories are provided to help the reader understand the rationale of the question, the design of the experiment, and data processing measures. If any theoretical/literature values are used, they should be introduced here.
A hypothesis consists of a justified prediction of the expected outcome and should be integrated with any background information.
- The **independent** variable is the variable that is explicitly changed to attempt to affect the dependent variable.
- The **dependent** variable is the variable that is directly monitored and measured in the experiment and is expected to change if the independent variable changes.
- **Controlled** variables (also known as "control variables") are variables that should be kept constant so they do not affect the dependent variable.
The independent variable, dependent variable, and any controlled variables should be listed under this section.
A list of materials and equipment should be listed here, as well as their precision. If a controlled variable needs to be measured, any instruments that would be used to do so should also be listed here.
A clear, detailed, and concise set of instructions written in *past tense* should be placed in this section as either a numbered list or descriptive paragraph. To reduce confusion, if a numbered list is used, referring directly to numbers should be avoided, and referring to numbers recursively must *never* happen. A procedure must include:
- a clear, titled, labelled, and annotated diagram
- instructions for recording data (including for controlled variables)
If necessary, a "setup" section can be added as preparatory steps should not be listed in the main procedure.
Data should be collected in an organised and titled table that should be prepared before the experiment. To reduce plagiarism, the data table must be verified by a teacher before leaving the lab space. After verification, **no new data** can be added. During an experiment that spans multiple days, this data must be verified every day. The data table must include:
- units with uncertainty, typically in the table header
- *qualitative* data (quantitative data can be optional in some experiments)
- repeated data/controlled variables, typically in the title
Only **raw data** prior to any processing or calculations, with the exception of averages, should be present in the data table.
A data table should be as concise as possible, and redundancy should be minimised. In that vein, trial numbers should *not* be recorded unless that data is relevant.
!!! example
**Effect of Fat Content on Sugar Content in Ice Cream**
A single sample calculation showing all steps should be present and clearly explained. The rest of the data can be processed without describing any steps. A **single** graph may be included if needed.
Some general rules include:
- units and uncertainties must be present in all calculations
- simple operations such as averages and conversions (e.g., g to kg) do not need to be explained
- the graph, if any, should span a full page and should directly answer the research question
A final, reorganised, and processed data table should be present here, showing only relevant information.
### Conclusion and evaluation
This section should be free of any new background information or calculations. It should, in sequence:
- summarise the results of the experiment without connecting it to the hypothesis
- identify whether the results of the experiment agree or disagree with the hypothesis
- evaluate 3–5 systematic errors (usually) present in the experiment, both in the procedure and in data collection/processing, in **decreasing** order of impact to the experiment
The evaluation of systematic errors should include:
- a description of the error
- how the error affected the data
- how the error affected the final result
- how the error can be remedied with available school resources
The title of a graph should clearly indicate what the graph represents under what conditions in **title case**, so that any onlooker should be able to identify the experiment. It should not include "vs." Any legends present should be located under the graph.
- The **effective nuclear charge** ($Z_\text{eff}$) is the net positive charge (attraction to the nucleus) experienced by an electron in an atom.
- **Electron shielding** describes the decrease in the effective nuclear charge of an electron because of the repulsion of other electrons in lower-energy shells.
**Atomic notation** is used to represent individual atoms or ions. It is written in the form $^M_Z \text{Symbol}^\text{Charge}$, where $M$ is the mass number of the particle and $Z$ is the atomic number of the particle.
!!! example
- $^1_1 \text{H}^{+}$ is the atomic notation for the most common hydrogen ion.
- $^{16}_8 \text{O}^{2-}$ is the atomic notation for the most common oxygen ion.
Isotopes are atoms of the same element but with different masses, or alternatively, atoms with the same number of protons but with different numbers of neutrons.
**Radioisotopes** are isotopes that are unstable (will spontaneously decay, are radioactive). Unstable atoms **decay** (break down) into one or more different isotopes of a different element. The **half-life** of a radioisotope is the time it takes for 50% of a sample's atoms to decay.
!!! warning
Radioisotopes are dangerous! They emit radiation, which is not at all good for human health in the vast majority of cases. However, there are also useful applications for radioisotopes today. For example, Cobalt-60 is used in radiation therapy to kill cancer tumours by damaging their DNA.
The mass of every atom is represented relative to 1/12th of a carbon-12 atom. This mass is either unitless or expressed in terms of **atomic mass units (amu or u)**. On the periodic table, the **relative atomic mass** ($A_r$) is shown, which is the sum of the masses of each isotope combined with their natural abundance (%abundance).
$$A_r = \text{%abundance}×\text{mass number of isotope}$$
$$m_a = \Sigma A_r$$
When calculating the atomic mass from the graph from a **mass spectrometer**, the sum of the natural abundances of each isotope may not equal 100 or 1 (not in %abundance). In this case, calculation of %abundance will need to be done before solving for $m_a$.
A mass spectrometer may also provide mass in the form of $M/Z$, which represents mass over charge. For the sake of simplicity, $Z=1$, so $M/Z$ represents the mass of a particle.
The atomic radius of an atom is the distance from the centre of the nucleus to approximately the outer boundary of the electron shell. This cannot be directly measured by scientists.
### Models
Please see [SL Physics#Models](/sph3u7/#models) for more information.
### Periodic trends
Some trends in the periodic table include:
- atomic radius decreases when going across a period
- atomic radius increases when going down a group
- ionic radius decreases when going across a period for groups 1–13, then sharply increases and then increases for groups 15–17
- ionic radius increases when going down a group
- electron affinity increases when going across a period
- electron affinity decreases when going down a group
- ionisation energy increases when going across a period
- ionisation energy decreases when going down a group
When explaining these trends in the periodic table, it is best to use basic concepts to build on to larger points.
!!! example
To explain why there is a trend of decreasing atomic radius across a period:
- As the number of protons and electrons increase together, but the number of electron shells does not change, the effective nuclear charge of each electron increases, while the effect of shielding remains unchanged.
- This increased effective nuclear charge reduces the atomic radius compared to other atoms before it.
