That is not an iPod Nano, but actually an Apple iPod Shuffle. Based on the design with a large, clickable control pad, it is likely a 2nd generation model, which came in a purple color option. 
Overview of the iPod Shuffle
Feature Details
Model TypeiPod Shuffle
GenerationLikely 2nd or 4th Generation (visually very similar)
ColorPurple or Lavender Purple
Storage CapacityTypically available in 1 GB or 2 GB models
DesignFeatures a lightweight, sleek, anodized aluminum enclosure with a built-in clip for wearing it on clothes or a bag
ControlsUses a physical, clickable control wheel for play/pause, volume, and skipping tracks
Battery LifeThe 2nd generation model offered up to 12 hours of audio playback, while the 4th generation could last up to 15 hours
Key FeaturesNo screen; later generations (4th and 5th) introduced a VoiceOver feature to announce song titles and playlist names
StatusApple discontinued the iPod Shuffle line in 2017, and the product is now considered obsolete
The iPod Nano, by contrast, had a screen and a different form factor, with the first generation having a plastic front and stainless steel back.