Physical constants (speed of light, Planck) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate energy of a photon using Planck's constant and frequency

Given the frequency of a photon as 5e14 Hz, what is the energy of this photon using Planck's constant from scipy.constants?

SciPy

from scipy.constants import h
frequency = 5e14
energy = h * frequency
print(energy)

A 1.5e-19

B 6.626e-34

C 3.313e-19

D 9.11e-31

💡 Hint

Energy of a photon is Planck's constant times frequency.

Energy = h * frequency. Using h = 6.62607015e-34 J·s and frequency = 5e14 Hz, energy = 3.313e-19 J.

❓ data_output

intermediate

Retrieve and display speed of light and Planck constant values

Using scipy.constants, what are the values of the speed of light and Planck constant printed as a tuple (speed_of_light, planck_constant)?

SciPy

from scipy.constants import c, h
print((c, h))

A (3.14e8, 6.626e-34)

B (3e8, 6.626e-34)

C (299792458, 1.602e-19)

D (299792458.0, 6.62607015e-34)

💡 Hint

Use scipy.constants.c and scipy.constants.h for exact values.

The exact speed of light is 299792458 m/s and Planck constant is 6.62607015e-34 J·s in scipy.constants.

🧠 Conceptual

advanced

Understanding units of Planck constant and speed of light

Which of the following correctly describes the units of Planck constant and speed of light?

A Planck constant: Joule seconds (J·s), Speed of light: meters per second (m/s)

B Planck constant: meters per second (m/s), Speed of light: Joule seconds (J·s)

C Planck constant: kilograms (kg), Speed of light: seconds (s)

D Planck constant: Newtons (N), Speed of light: meters (m)

💡 Hint

Think about what Planck constant and speed of light physically represent.

Planck constant measures energy-time product, so units are Joule seconds. Speed of light is a velocity, so meters per second.

🔧 Debug

advanced

Identify the error in this code using scipy.constants

What error does the following code produce? from scipy.constants import speed_of_light print(speed_of_light)

SciPy

from scipy.constants import speed_of_light
print(speed_of_light)

A ImportError: cannot import name 'speed_of_light'

B NameError: name 'speed_of_light' is not defined

C AttributeError: module 'scipy.constants' has no attribute 'speed_of_light'

D No error, prints 299792458.0

💡 Hint

Check the exact name of the constant in scipy.constants.

The correct name is 'c' for speed of light, not 'speed_of_light'. Importing 'speed_of_light' causes ImportError.

🚀 Application

expert

Calculate wavelength from photon energy using scipy.constants

Given a photon energy of 4e-19 Joules, calculate the wavelength in meters using Planck constant and speed of light from scipy.constants. Which option is the correct wavelength?

SciPy

from scipy.constants import h, c
energy = 4e-19
wavelength = (h * c) / energy
print(wavelength)

A 7.50e-07

B 4.97e-07

C 1.24e-06

D 3.31e-19

💡 Hint

Use wavelength = (Planck constant * speed of light) / energy.

Wavelength = (h * c) / energy = (6.62607015e-34 * 299792458) / 4e-19 ≈ 4.97e-07 meters.

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