Physical constants (speed of light, Planck) in SciPy - Step-by-Step Execution

Concept Flow - Physical constants (speed of light, Planck)

Import scipy.constants

↓

Access constant: speed_of_light

↓

Access constant: Planck constant

↓

Print or use constants in calculations

↓

End

The flow shows importing the constants module, accessing specific constants, and using them.

Execution Sample

SciPy

from scipy.constants import speed_of_light, h

print(speed_of_light)
print(h)

This code imports and prints the speed of light and Planck constant values.

Execution Table

Step	Action	Evaluation	Result
1	Import speed_of_light and h from scipy.constants	Module loads constants	speed_of_light and h available
2	Print speed_of_light	speed_of_light value accessed	299792458.0
3	Print h	h value accessed	6.62607015e-34
4	End of code	No more statements	Execution stops

💡 All constants accessed and printed, program ends

Variable Tracker

Variable	Start	After Step 2	After Step 3	Final
speed_of_light	Not defined	299792458.0	299792458.0	299792458.0
h	Not defined	Not defined	6.62607015e-34	6.62607015e-34

Key Moments - 2 Insights

Why do we import constants instead of defining numbers ourselves?

Importing from scipy.constants ensures we use exact, standard values, avoiding errors from manual typing. See execution_table step 1 where constants become available.

Why is speed_of_light a large number but Planck constant very small?

Speed of light is measured in meters per second (large scale), Planck constant is a quantum scale value (very small). See execution_table steps 2 and 3 for their values.

Visual Quiz - 3 Questions

Look at the execution table, what is the value of speed_of_light at step 2?

A 6.62607015e-34

B 299792458.0

C 3.0e8

D Not defined yet

💡 Hint

Check execution_table row with Step 2 under Result column

At which step does Planck constant become available?

A Step 2

B Step 3

C Step 1

D Step 4

💡 Hint

See execution_table step 1 where constants are imported

If we print h before importing, what happens?

A Raises an error

B Prints zero

C Prints the correct value

D Prints None

💡 Hint

Variables must be defined before use, see variable_tracker initial states

Concept Snapshot

Use scipy.constants to access physical constants.
Import constants like speed_of_light, h.
Values are precise and standard.
Use them directly in calculations or print.
Avoid manual typing to prevent errors.

Full Transcript

This example shows how to use the scipy.constants module to get physical constants like the speed of light and Planck constant. First, we import these constants from scipy.constants. Then, we print their values. The speed of light is a large number in meters per second, while Planck constant is very small, reflecting their physical meanings. Importing constants ensures accuracy and avoids mistakes from manual entry. The execution table traces each step: importing, accessing, printing, and ending. The variable tracker shows when each constant becomes available. Common confusions include why we import constants and the difference in magnitude between constants. The quiz checks understanding of values and import timing.

Practice

1. What is the value of the speed of light constant c in scipy.constants measured in?

easy

A. Meters per second

B. Kilometers per hour

C. Miles per second

D. Feet per second

Solution

1. Step 1: Understand the unit of speed of light in scipy.constants

   The speed of light c in scipy.constants is given in meters per second (m/s), which is the standard SI unit for speed.

2. Step 2: Confirm the unit from official documentation or usage

   Checking the official scipy documentation confirms c is in meters per second.

3. Final Answer:

   Meters per second -> Option A

4. Quick Check:

   Speed of light unit = meters per second [OK]

Hint: Speed of light is always in meters per second [OK]

Common Mistakes:

• Confusing meters per second with kilometers per hour
• Assuming miles or feet units
• Not checking scipy documentation

2. Which of the following is the correct way to import and access Planck's constant from scipy.constants?

easy

A. import scipy.constants; scipy.constants.planck

B. import scipy.constants as sc; sc.Planck

C. from scipy.constants import Planck

D. from scipy.constants import planck

Solution

1. Step 1: Recall the exact attribute name for Planck's constant

   In scipy.constants, Planck's constant is accessed as planck (all lowercase).

2. Step 2: Check import syntax correctness

   import scipy.constants; scipy.constants.planck uses import scipy.constants and accesses scipy.constants.planck, which is correct. from scipy.constants import planck tries to import planck directly, which is valid but not the exact syntax shown here. import scipy.constants as sc; sc.Planck uses incorrect capitalization Planck. from scipy.constants import Planck also uses wrong capitalization and import style.

3. Final Answer:

   import scipy.constants; scipy.constants.planck -> Option A

4. Quick Check:

   Correct attribute name is planck, accessed via scipy.constants [OK]

Hint: Planck constant is lowercase 'planck' in scipy.constants [OK]

Common Mistakes:

• Using uppercase 'Planck' instead of lowercase
• Incorrect import syntax
• Trying to import planck directly without correct syntax

3. What is the output of this code snippet?

from scipy.constants import c, planck
wavelength = 500e-9  # 500 nm in meters
energy = planck * c / wavelength
print(round(energy, 20))

medium

A. 3.972891714285714e-16

B. 3.972891714285714e-25

C. 3.972891714285714e-22

D. 3.972891714285714e-19

Solution

1. Step 1: Calculate photon energy using formula E = h * c / wavelength

   Given wavelength = 500 nm = 500e-9 m, Planck's constant (h) and speed of light (c) are constants from scipy.constants. Calculate energy = planck * c / wavelength.

2. Step 2: Perform calculation and round result

   Using scipy.constants values: planck ≈ 6.62607015e-34, c ≈ 299792458, energy ≈ (6.62607015e-34 * 299792458) / 500e-9 = 3.972891714285714e-19 J. Rounded to 20 decimals matches 3.972891714285714e-19.

3. Final Answer:

   3.972891714285714e-19 -> Option D

4. Quick Check:

   Energy = h*c/wavelength = 3.97e-19 J [OK]

Hint: Use E = h*c/wavelength formula with correct units [OK]

Common Mistakes:

• Forgetting to convert nm to meters
• Mixing up multiplication and division
• Rounding too early or incorrectly

4. Identify the error in this code snippet that tries to calculate photon energy:

from scipy.constants import Planck, c
wavelength = 600e-9
energy = Planck * c / wavelength
print(energy)

medium

A. Missing import for speed of light

B. Wavelength should be in nanometers, not meters

C. Planck constant is incorrectly capitalized

D. Division operator should be multiplication

Solution

1. Step 1: Check import statement for Planck constant

   The code imports Planck with uppercase 'P', but in scipy.constants it is lowercase planck. This causes an AttributeError.

2. Step 2: Verify other parts of the code

   Wavelength is correctly converted to meters (600e-9), speed of light c is imported correctly, and the formula uses correct division. So no other errors.

3. Final Answer:

   Planck constant is incorrectly capitalized -> Option C

4. Quick Check:

   Correct attribute is 'planck' lowercase [OK]

Hint: Check exact case for constants in scipy.constants [OK]

Common Mistakes:

• Using uppercase 'Planck' instead of lowercase
• Confusing units of wavelength
• Wrong operator in formula

5. You want to calculate the energy of a photon with wavelength 400 nm using scipy.constants. Which code snippet correctly computes and prints the energy in electronvolts (eV)?

hard

A. from scipy.constants import c, planck
wavelength = 400e-9
energy_ev = planck * c / wavelength
print(round(energy_ev, 3))

B. from scipy.constants import c, planck, electron_volt
wavelength = 400e-9
energy_joule = planck * c / wavelength
energy_ev = energy_joule / electron_volt
print(round(energy_ev, 3))

C. from scipy.constants import c, planck, electron_volt
wavelength = 400
energy_joule = planck * c / wavelength
energy_ev = energy_joule * electron_volt
print(round(energy_ev, 3))

D. from scipy.constants import c, planck
wavelength = 400e-9
energy_joule = planck * c * wavelength
print(round(energy_joule, 3))

Solution

1. Step 1: Calculate photon energy in joules using E = h*c / wavelength

   Use wavelength in meters (400e-9). Calculate energy_joule = planck * c / wavelength.

2. Step 2: Convert energy from joules to electronvolts

   Divide energy_joule by electron_volt constant to get energy in eV.

3. Step 3: Check code correctness

   from scipy.constants import c, planck, electron_volt wavelength = 400e-9 energy_joule = planck * c / wavelength energy_ev = energy_joule / electron_volt print(round(energy_ev, 3)) correctly imports electron_volt, converts units properly, and prints rounded value. Other options either miss conversion, use wrong wavelength units, or wrong formula.

4. Final Answer:

   from scipy.constants import c, planck, electron_volt wavelength = 400e-9 energy_joule = planck * c / wavelength energy_ev = energy_joule / electron_volt print(round(energy_ev, 3)) -> Option B

5. Quick Check:

   Energy (eV) = (h*c/wavelength)/electron_volt [OK]

Hint: Convert joules to eV by dividing by electron_volt constant [OK]

Common Mistakes:

• Skipping conversion from joules to eV
• Using wavelength in nm without converting to meters
• Multiplying instead of dividing for energy calculation