With the same matched line, three calibration scales move the displayed detector channel. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Scale changes the detector channel

The photon energy stays 5 joules and the offset stays 1 channel. Scale 1 maps the line to channel 6.

channel=15+1=5+1=6channel=1\cdot 5 + 1=5 + 1=6
Calibration scale scanThe same line moves when the channel scale changes.E=5 Jchannel=6scale=1lowerupper5

Scale changes the detector channel

The photon energy stays 5 joules and the offset stays 1 channel. Scale 2 maps the line to channel 11.

channel=25+1=10+1=11channel=2\cdot 5 + 1=10 + 1=11
Calibration scale scanThe same line moves when the channel scale changes.E=5 Jchannel=11scale=2lowerupper5

Scale changes the detector channel

The photon energy stays 5 joules and the offset stays 1 channel. Scale 3 maps the line to channel 16.

channel=35+1=15+1=16channel=3\cdot 5 + 1=15 + 1=16
Calibration scale scanThe same line moves when the channel scale changes.E=5 Jchannel=16scale=3lowerupper5