Significant Figures
When are zeros significant?
When a) they are sandwiched between 2 digits between 1 and 9 and b) when they are trailing zeros in a decimal (so at the end).
Write the following in either scientific notation or standard form
7 x 10^3
5326.6
5.1996 x 10^0
0.000001031
42.9 x 10^-4
Double check your work with a partner. How are you doing?
Light acts as both a particle and a wave. What are the distinguishing behaviors of each?
Waves will reflect and refract.
Particles will be emitted and either stop or go through things.
What is the relationship between wavelength and energy?
The shorter the wavelength, the more energy
(Inverse relationship)
In the formulas we use to solve for energy problems, what are the units for:
- energy
- wavelength
- frequency
Energy = Joules (J)
Wavelength = meters (m), if not in meters we must convert our units
Frequency = Hertz (Hz)
For the following, identify the # of significant figures:
956
2.1390
4903
0.500
3670000
0.0000620
Remember: Nonzero digits are always significant. Zeros only when they are sandwiched between nonzero digits or when they're at the end of a decimal.
Are the following expressions written in scientific notation? Why or why not?
0.325 x 10^-7
4.7 x 10^3
13.13 x 10^-33
2 x 10^0
6.1 x 10^2.5
Proper scientific notation is written with number between 1 and 10 (except actual 10), followed by 10 to the power of an integer.
Integer: whole number
What is visible light?
The tiny part of the electromagnetic spectrum, energy in the form of electromagnetic radiation we can actually see
○ Wavelengths between 400 nm and 700 nm
What is wave frequency?
Wave frequency is the number of waves that pass a fixed point in a given amount of time, usually a second.
Convert 2 yards to centimeters
You have to convert 3 times.
1 yard = 3 feet
1 foot = 12 inches
1 inch = 2.54 cm
Round the following numbers to 3 significant figures:
67.21
17520
0.06111
0.002998
2296000
0.007896
Note: Rounding off to x significant digits does not mean that we only have x amount of #s
With whole #s, we simply add zeros to fill in blanks
With decimals, we crop after rounding
Solve the following:
(1.3 x 10^2)(2.5 x 10^9)
(4.2 x 10^-13)(1.6 x 10^4)
Remember: When multiplying in scientific notation, we add the exponents. Be careful with negatives.
Compare the colors black and white.
White reflects all colors/ wavelengths while black absorbs them all.
What color of the rainbow has the lowest frequency? The highest?
How do you know?
Lowest = red
Highest = violet
You should know the relationship between wavelength and frequency.
A photon of violet light has a wavelength of 0.04 cm.
Calculate its energy.
Ha, you thought. Go check the notes :P
Solve the problem following the adding/ subtracting rule for significant figures:
145 - 0.222
1.25 + 3.2
Note: Our final answer should be rounded to have the same # of decimals as the # with the least specificity
Solve the following:
(5.3 × 10^-13) / (7.65 × 10^5)
(7.6 × 10^0) / (5.4 × 10^−6)
Remember: When dividing in scientific notation, we subtract the exponents. Be careful with negatives.
What 2 characteristics do all waves have in
common?
1. they all have the wave-particle duality
2. they all travel at c, the speed of light
Order the following from least to greatest energy:
- visible light
- gamma rays
- infrared
- microwaves
- ultraviolet
1) Microwaves
2) Infrared
3) Visible light
4) Ultraviolet
5) Gamma
Compare the terms redshift and blueshift. What characterizes each and what do they tell us about the location of an object?
Double check with w11 notes :)
Solve the problem following the multiplying/ dividing rule for significant figures:
3340 x 1.2
88359 / 3
Note: Our final answer should be rounded to the least # of sig figs.
Solve the following:
(5.2 x 10^2) + (3 x 10^3)
(18.45 x 10^-7) - (6.9 x 10^-7)
Remember: Exponents must be the same before adding/subtracting. Also check that your final answer is in proper scientific notation.
At a microscopic level, when is light created?
When an electron within an atom that is in an excited state drops to a lower energy state (ground state) and loses this excess energy.
Why is space dark if there's so many stars?
Space is dark because light is only visible when it has an object of which to bounce off. Otherwise, it will continue to move at the speed of light.
Also, even though there's so many stars, their light is so far away that it has not had had time to reach us yet and so can't contribute to making the sky bright.
What is the energy and frequency of a green light wave being reflected off the projector if its wavelength is 593 nanometers.
3 steps:
1) convert wavelength to meters
2) solve for frequency
3) solve for energy