E = m c 2

1. E = m c2 Lab 6 Homework Formulas

2. Formulas • In Science, problems maybe solved by entering measurements into formulas. • Formula represent a mathematical relationship between quantities that are derived from laws or theories. • In E= mc2, Einstein calculated the amount of energy (E) that would be released if a certain mass (m) was converted to energy and that the amount was directly proportional to the mass and at a constant rate (c-for constant)-the speed of light (c) squared.

3. Volume • The volume (V) of most regular rectangular objects if found by multiplying the length (l) by the width (w) and the height or thickness (h) of the object in the formula: V = l · w · h.

4. Volume • What is the volume of a rectangular block of metal that is 12.0 cm long, 30.0 cm wide and 5.1 cm high ? • V = l · w · h = (l)(w)(h) = (12.0 cm)(30.0 cm)(5.1 cm) = 1836 cm3 • BUT since the height only has two (2) significant figures the answer is 1800 cm3! 3 sig. figs. 3 sig. figs. 2 sig. figs.

5. Density • Density is the compactness of an object. The amount of mass crammed into a certain space of volume. The mass per unit of volume. Per means to divide. So • D = m / V

6. Density • What is the density of a rock that has a mass (m) of 18.203 grams (g) and occupies a volume of 16.0542 cubic centimeters (cm3)? • D = m / V = 18.203 g / 16.0542 cm3 = 1.13384659466 g / cm3 on the calculator, BUT since the mass only has 5 significant figures, the answer is 1.1338 g/ cm3 6 sig. figs. 5 sig. figs.

7. Speed • Speed or rate (r) is the distance (d) a moving object covers in a specific amount of time. Speed is a scalar or undirected quantity. • Velocity (v) is the displacement (s) a moving object covers in a directions in a specific amount of (t). Displacement and thus Velocity are vector or directed quantities. • They are computed similarly, but with different formulas to denote scalar or vector quantities.

8. Speed II • Distance (d) is the product (product means multiplication) of the speed or rate (r) and the time (t). D = rt = r · t = (r)(t) • Displacement (s) is the product of velocity (v) and time (t). s= vt = v · t = (v)(t) • How much distance does a space vehicle cover in 1.000 hrs traveling at 10850 km / hr (orbital speed)? D=rt= (10850 km/hr) (1.000hr) =1085 km. 4 sig figs. 5 sig. figs. 4 sig figs

9. Speed of Light • The speed of light is 3.00 X 10 8 m/s. (186,272 miles/s) in a vacuum (space). • When light (white) passes through a more dense medium such as a gas ( or air) or water or a glass, the speed is reduced that the light is refracted or bent. If refracted enough, it will undergo dispersion, that is the white light will be separated into it’s color components.

10. Dispersion White light is dispersed into the basics colors of purple, blue, green, yellow, orange and red. Red light is bent and dispersed more than Blue light. A rainbow is the dispersion of sunlight by drops of rain .

11. Light • White light is a combination of all the colors. • Since the speed of light is 3.00 X 108 m/s, (c) , the speed of its colors is also this. • Since light has wave characteristics, it and its colors have wavelength (λ) in meters (m) -usually nanometers (nm) and Angstroms (Å), and frequency (f) in hertz (Hz) or cycles per second ( /s).

12. Frequency • 1000 Hz = 1 X 103Hz = 1 kilo hertz (1 kHz) • 1,000,000 Hz = 1 X 106Hz = 1 Mega hertz (MHz) • 1,000,000,000 Hz = 1 X 109Hz = 1 Giga hertz (GHz) • 1,000,000,000,000 Hz = 1 X 1012Hz = 1 Tera hertz (THz) • NOTE: 1 X 1013 Hz = 1 X 1012 · 10Hz = 1· 10 X 1012 Hz = 10 Tera hertz or 10 THz.

13. Spectral Colors Continuous spectrum

14. Colors The picture about is the dispersed light from the sun, which is a glowing gas, and it thus termed a continuous spectrum. Notice the range of colors, their wavelength in nm and their energy in eV. eV is related to their frequency. The instrument that displays and measure the spectrum is a spectrophotometer.

15. Frequency and Wavelength • Violet light has a average wavelength of 415nm (4150 Å). What is the frequency of violet light? • From c = f λ f = c / λ *Note c is the speed of light in meter/ second and λ is in nanometers. Convert 415 nm to meters and we get 4.15 X 10-7m.

16. 3.00 X 108m/s3.00 X 108 /s f = = = 4.15 X 10-7m 4.15 X 10-7 3.00 X 108 · /s** = /s = 0.723 · X 10(8-(-7))* 4.15 X 10-7 0.723 X 1015Hz = 7.23 X 1013 Hz Answers or 7.23 X 1012· 10 Hz = 7.23 ·10 X 1012 Hz = 72.3 X 1012 Hz = 72.3 THz *10(8-(-7) = 10(8+7) = 1015 ** /s = Hz

17. Frequency and Wavelength II Green light has a average frequency ( f ) of 566 THz. What is the wavelength( λ ) of Green light in nanometers (nm)? Convert THz to Hz Then to /s. Find wavelength in meters (m). Convert m to nm.

18. 566 THz = 566 X 1012 Hz = 5.66 X 1014Hz = • 5.66 X 1014 /s 2. c = fλλ = c / f 3.00 X 108 m/s 3.00 5.66 108 1014 c = = · m = 5.66 X 1014 /s 0.530 X 10(8-14) m = 0.530 X 10-6 m = 5.30 X 10-7 m 3. 5.30 X 10-7m109nm5.30 X 10-7+9 nm 1 1 m 1 = 5.30 X 102nm = ·

19. Energy and frequency The frequency of a wave or color determine its energy. The faster the frequency the more energy the wave or color has. So, f E. Enter Max Planck’s quantum equation: E = hf (p. A-3 of textbook) The Energy of a wave, a color or photon* is the product of the frequency (f) and Planck’s Constant (h). Page A-2 of the textbook give h its value of: 6.63 X 10-34 j·s (joule second).

20. Energy of Color • How much energy does Orange light have? • Find the average frequency of Orange Light. Change to /s • Use Planck’s equation to find the energy • If necessary to find the energy in eV, convert J to eV.

21. Frequency of Orange light is average of low and high frequencies: 496 THz. 496 · 1012 Hz or • 4.96 X 1014 Hz = 4.96 X 10 14/s. • 2. E = hf = 6.63 X 10-34j · s · 4.96 X 10 14 /s = • 6.63 · 4.96 x10-34+14j ·s/s = 32.8 X 10-20 j = • 3.28 X 10-19 j • 3.28 X 10-19 j 1 eV _ • 1 1.60 X 10-19 j • 3.28X 10-19 • 1.60 X 10-19 · = · eV = 2.05 eV

22. THE END Lab 6 Homework USING FORMULA IN ASTRONOMY