import math def translation_partition_function(mass: float, temperature: float, volume: float) -> float: """ Calculates the translational partition function using the formula: q_trans = ((2 * pi * m * k_B * T)^(3/2) * V) / h^3 mass: Mass of the molecule in kg temperature: Temperature in Kelvin volume: Volume in cubic meters >>> round(translation_partition_function(2e-26, 300, 1e-3), 4) 4.081816847078438e+28 >>> round(translation_partition_function(4e-26, 300, 1e-3), 4) 1.1545121488522627e+29 >>> round(translation_partition_function(-4e-26, 300, 1e-3), 4) Traceback (most recent call last): ... ValueError: Mass must be positive >>> round(translation_partition_function(4e-26, 0, 1e-3), 4) Traceback (most recent call last): ... ValueError: Temperature must be positive >>> round(translation_partition_function(4e-26, 300, 0), 4) Traceback (most recent call last): ... ValueError: Volume must be positive """ if mass <= 0: raise ValueError("Mass must be positive") if temperature <= 0: raise ValueError("Temperature must be positive") if volume <= 0: raise ValueError("Volume must be positive") h = 6.62607015e-34 # Planck's constant in J·s k_B = 1.380649e-23 # Boltzmann constant in J/K prefactor = (2 * math.pi * mass * k_B * temperature) ** (3 / 2) denominator = h ** 3 return (prefactor * volume) / denominator if __name__ == "__main__": import doctest doctest.testmod(name="translation_partition_function")