Tungsten–halogen source stability in spectrophotometry: why must the supply voltage to a tungsten lamp be very stable during measurements?

Introduction / Context:
Tungsten and tungsten–halogen lamps are common continuum sources in visible–near-IR spectrophotometers. Signal accuracy relies on stable source intensity, which depends strongly on lamp operating conditions.

Given Data / Assumptions:

• Filament temperature rises with applied voltage/current.
• Radiant exitance of a hot filament scales steeply with temperature (Stefan–Boltzmann-type behavior).
• In practice, lamp radiant output varies very strongly with small voltage changes.

Concept / Approach:
Because filament temperature responds nonlinearly to voltage, even small voltage ripple produces large intensity fluctuations. This translates directly into absorbance noise and baseline drift. Therefore, regulated power supplies are essential.

Step-by-Step Solution:
Recognize sensitivity: a few percent voltage change can cause tens of percent intensity change.Link to spectrophotometry: intensity instability corrupts P and P0, degrading A = log10(P0 / P) precision.Conclusion: ensure highly regulated voltage to maintain constant filament temperature and output.

Verification / Alternative check:
Instrument specifications often cite lamp voltage regulation and warm-up time to achieve stable baselines.

Why Other Options Are Wrong:
Immediate burnout (a) is exaggerated and not the primary reason. Single fixed voltage operation (c) is false; lamps have ranges. Option e is incorrect because intensity, not wavelength, is most affected.

Common Pitfalls:
Assuming double-beam configurations fully cancel source instability; they reduce but do not eliminate intensity noise without stable power.

Final Answer:
Because the radiant output is extremely sensitive to operating voltage (approximately a fourth-power dependence).